The 1730s decade ran from January 1, 1730, to December 31, 1739.
- January 29 – Anna Ivanovna (Anna of Russia) becomes empress, following the death of her cousin, Emperor Peter II.
- February 26 – (February 15 O.S.)Anna Ivanova becomes the new Empress of Russia upon the death of Emperor Peter II.
- February 28 – Vitus Bering returns to the Russian capital of Saint Petersburg after completing the First Kamchatka expedition.
- March 5 – The conclave to elect a new Pope begin with 30 Roman Catholic Cardinals, 12 days after the death of Pope Benedict XIII. By the time his successor is elected on July 12, there are 56 Cardinals.
- March 9 – General Nader Khan of Persia opens the first campaign of the Ottoman–Persian War, guiding the Persian Army from Shiraz and starting the Western Persia Campaign to fight the Ottoman Empire.
- March 12 – John Glas is deposed from the Church of Scotland; the Glasite sect forms around him.
- March 16 – The establishment by Thomas Cresap of Wright's Ferry under the authority of the Province of Pennsylvania  becomes the basis for Cresap's War – a nine-year-long conflict also known as the Maryland-Pennsylvania boundary dispute – the conflict mainly centers in Lancaster County, Pennsylvania and York County, Pennsylvania on either banks of the Susquehanna River.
- April 8 – Shearith Israel, the first synagogue in New York City, is dedicated.
- May 9 – (April 28 O.S.) The coronation of Anna of Russia as Empress of Russia takes place in Saint Petersburg.
- May 15 – Charles Townshend, 2nd Viscount Townshend, retires from his role in the government of Great Britain, leaving Robert Walpole as sole and undisputed leader of the Cabinet (i.e., prime minister). In the new Walpole ministry, Sir William Strickland, 4th Baronet, becomes Secretary at War, and Henry Pelham is Paymaster of the Forces. Spencer Compton, 1st Earl of Wilmington briefly becomes Lord Privy Seal.
- June 1 – Enslaved woman Sally Bassett is put on trial in Bermuda; she would eventually be convicted and burned at the stake.
- June 19 – At the urging of Sir William Gooch, the Virginia House of Burgesses passes the Virginia Tobacco Inspection Act to regulate the quality of Virginian tobacco passes, 46 to 5.
- June 27 – French explorer Alphonse de Pontevez, commanding the frigate Le Lys, claims an Indian Ocean atoll for France and names it after himself as the Alphonse Atoll. The next day, he claims and names the St. François Atoll.
- July 8 – An earthquake with an estimated magnitue of 9.1 strikes Valparaiso, now part of Chile but at the time located in the Viceroyalty of Peru.
- July 12 – The papal conclave selects Cardinal Lorenzo Corsini over Cardinal Pietro Marcellino Corradini as the successor to Pope Benedict XIII. Corsini becomes Pope Clement XII as the 246th pope.
- August 4 – Maria Madlener becomes the last person to be executed after the Galgeninsel witch trials in Bavaria, and is beheaded by sword.
- August 5 – Prince Frederick of Prussia, the eldest son of King Frederick William and a high-ranking officer, attempts to flee to England after deserting the Prussian Army and is captured along with his fellow officer Hans Hermann von Katte. Katte is executed, and Crown Prince Frederick is imprisoned at Küstrin (now Kostrzyn nad Odrą in Poland) for a year before being forgiven by his father. Prince Frederick later succeeds his father as King and is now remembered as Frederick the Great.
- August 12 – General Nader Khan of Persia captures Tabriz from the Ottoman Empire, bringing an end to the Western Persia Campaign, the first major action in the Ottoman–Persian War. Tabriz has been part of Iran ever since. Nader leaves Tabriz four days later to begin the Herat Campaign.
- August 25 – French Protestant Marie Durand is imprisoned in the Tower of Constance at Aigues-Mortes for her defiance of the Roman Catholic government, and keeps her captive for the next 38 years. During her incarceration, she continues to resist converting to Catholicism as a condition of release. She is finally set free on April 14, 1768 and lives 8 more years.
- September 1 – A volcano erupts on Lanzarote, the easternmost of the Canary Islands and threatens the Spanish inhabitants. On Gran Canaria, the regent of the islands reports to Madrid that the flames are visible even from 130 miles (210 km) away.
- September 17 – Mahmud I (1730–1754) succeeds Ahmed III (1703–1730), as Ottoman Emperor.
- October 22 – Construction of the Ladoga Canal, linking the Neva and Svir Rivers, one of the first major navigable canals constructed in Russia, is completed.
- January 8 – An avalanche from the Skafjell mountain causes a massive wave in the Storfjorden fjord in Norway that sinks all boats that happen to be in the water at the time and kills people on both shores. 
- January 25 – A fire in Brussels at the Coudenberg Palace, at the time the home of the ruling Austrian Duchess of Brabant, destroys the building, including the state records stored therein.
- February 16 – In China, the Emperor Yongzheng orders grain to be shipped from Hubei and Guangdong to the famine-stricken Shangzhou region of Shaanxi province.
- February 20 – Louise Hippolyte becomes only the second woman to serve as Princess of Monaco, the reigning monarch of the tiny European principality, ascending upon the death of her father Prince Antonio. She reigns only nine months before dying of smallpox on December 29.
- March 16 – The Treaty of Vienna is signed between the Holy Roman Empire, Great Britain, the Dutch Republic and Spain.
- April 1 – Battle of Dabhoi in India is fought between Sarsenapati Trimbakrao Dabhade and Bajirao Peshwa.
- April 2 – The town of Raynham, Massachusetts in Bristol County is entered as a new town by the governor and court of Massachusetts, New England, America.
- April 9 – British trader Robert Jenkins has his ear cut off after his ship, Rebecca is boarded by Spanish coast guards at Havana in Cuba. ' The incident becomes the casus belli for the War of Jenkins' Ear in 1739. 
- April 28 – A fire at White's Chocolate House, near St. James's Palace, destroys the historic club and the paintings therein, but is kept from spreading by the fast response of firemen.
- May 10 – The Pacific Fleet of the Russian Navy is established by order of the Empress Anna of Russia, who directs Grigory Skonrnyakov-Pisarev to assume command over the new fleet and to develop Okhotsk as a major port. 
- June 4 – The English market town of Blandford Forum is destroyed by fire, with the exception of 26 houses. About one-third of the uninsured losses are paid for by the collection of disaster relief money. 
- July 1 – Benjamin Franklin and fellow-subscribers start the Library Company of Philadelphia.
- August 15 – King Frederick William I of Prussia forgives his 19-year-old son, Prince Frederick, who has been confined since November to the town of Küstrin (now Kostrzyn nad Odrą in Poland) for his 1730 attempt to desert from the Prussian Army.  Nine years later, having been politically rehabilitated, Prince Frederick succeeds his father as King and is later remembered as "Frederick the Great".
- August 23 – The oldest known sports score in history is recorded in the description of a cricket match at Richmond Green in England, when the team of Thomas Chambers of Middlesex defeats the Duke of Richmond's team, 119 to 79.
- September 30 – The village of Barnwell, Cambridgeshire, is "burned down entirely" by a fire. 
- October 23 – A fire at Ashburnham House in Westminster destroys 114 irreplaceable manuscripts (including a manuscript of the Anglo-Saxon Chronicle) and damages 98 others (among them the manuscript of Beowulf). Dr. Richard Bentley, the King's librarian and the House's owner, saves the only copy of the Codex Alexandrinus, carrying it under one arm as he leaps from a window. Dr. Bentley's ten year labor in translating the Greek Testament is ruined by the blaze. The remaining 844 manuscripts later form the heart of the collections of the British Library. 
- November 25 –
- Swiss mathematician Leonhard Euler announces his use of the irrational number e (approximately 2.71828) as the base for the concept of the natural logarithm, describing it in a letter to German mathematician Christian Goldbach.
- Patrona Halil, an ethnic Albanian and a janissary who instigated a mass uprising in 1730 within the Ottoman Empire that brought Mahmud I to power as the new Sultan, is strangled to death in Mahmud's presence after the rebellion is finally suppressed.
- December 21 – The Maharaja Chhatrasal, monarch of Bundelkhand in India (now part of the states of Uttar Pradesh and Madhya Pradesh) dies at the age of 82. His kingdom is divided into four parts, with one part going to Baji Rao I of the Marathas. The other three going to his three sons: Harde Sah gets the Panna State, Jagat Rai gets the Jaitpur State and Bharti Chand gets the Jaso State.
- December 29 – Jacques Grimaldi, the husband of the reigning monarch of Monaco, Louise Hippolyte, succeeds to the throne after Louise's death from smallpox. Jacques I rules until his own death in 1751. The House of Grimaldi has ruled the European principality for almost three centuries. The current ruler, Prince Albert II, is the great-great-great-great-great-great-great-grandson of Jacques.
- Royal Colony of North Carolina Governor George Burrington asks the North Carolina General Assembly to pass an act establishing a town on the Cape Fear River, in what is seen as a political move to shift the power away from the powerful Cape Fear plantation class. The town is laid out in 1733, and incorporated as Wilmington in 1740.
- English Captain Charles Gough rediscovers Gough Island in the South Atlantic.
- Laura Bassi becomes the first official female university teacher, on being appointed professor of anatomy at the University of Bologna, at the age of 21.
- John Bevis observes the Crab Nebula for the first time in the modern era.
- The Royal Theatre of Mantua (Italy) is built by Ferdinando Galli Bibiena.
- January 21 – Russia and Persia sign the Treaty of Riascha at Resht. Based on the terms of the agreement, Russia will no longer establish claims over Persian territories.
- February 9 – The Swedish East India Company begins its profitable first expedition to China, departing Gothenburg on the ship Friedericus Rex Sueciae under the command of Colin Campbell.
- February 14 – Henry Fielding's comedy The Modern Husband premieres at the Royal Theatre on Drury Lane in London.
- February 25 – John Stackhouse is appointed by the British East India Company as the new President of the Bengal Presidency and serves for seven years.
- February 27 – King Nader Shah of Persia (now Iran) suppresses the rebellion by Zulfiqar Khan in the city of Heran in what is now Afghanistan. 
- March 19 – Chamaraja Wodeyar VII becomes the new Maharaja of the Kingdom of Mysore in Southern India, now the state of Karnataka and parts of Tamil Nadu and Andhra Pradesh.
- March 30 – MPs John Birch and Denis Bond are expelled from the House of Commons of Great Britain after using their positions on the Commission for Forfeited Lands to make fraudulent sales.
- April 12 – King Christian VI of Denmark signs the charter for the new Danish Asia Company (Dansk Asiatisk Kompagni), granting it a 40-year monopoly on Denmark's trade in Asia, leading to the creation of Danish India and cities of Trankebar (now Tharangambadi in Tamil Nadu), Frederiknagore (now Serampore in West Bengal) and the Frederiksøerne Islands (now the Nicobar Islands).
- April 16 – After his disastrous attempt to fight the Ottoman Empire, Shah Tahmasp II is removed from the throne of Iran by one of his generals, Nader Khan, who later proclaims himself the King of Persia in Tahmasp's place as Nader Shah.
- May 10 – Representatives of the heirs of William Penn and of Lord Baltimore, the respective owners of most of the land in the Province of Pennsylvania and the Maryland Colony set out the boundary between the two future U.S. states after a survey determines that Philadelphia is located on the Maryland side of the border. The dispute eventually leads to a lawsuit and the eventual survey by Charles Mason and Jeremiah Dixon to determine the Mason–Dixon line.
- May 13 – Rebels in Corsica agree to allow the Republic of Genoa to resume its administration of the island in return for amnesty and promised reforms.
- May 28 – Dirck van Cloon becomes the new Governor-General of the Dutch East Indies (now Indonesia).
- June 9 – James Oglethorpe is granted a royal charter for the colony of Georgia.
- July 2 – Spain completes the conquest of the Algerian cities of Oran and Mers El Kébir in the Oran Province, after a 17-day siege.
- August 21 – Mikhail Gvozdev in the Sviatoi Gavriil makes the first known crossing of the Bering Strait, from Cape Dezhnev to Cape Prince of Wales in Alaska, marking the first time that Europeans have reached the northwest coast of North America. 
- September 13 – The Treaty of the Three Black Eagles or the Treaty of Berlin, a secret treaty between the Austrian Empire, the Russian Empire and Prussia against Polish–Lithuanian Commonwealth.
- September 16 – The magnitude 5.8 Montreal earthquake occurs in Quebec (New France).
- October 7 – French Army Lieutenant General Florent-Jean de Vallière is tasked by King Louis XV to improve France's method of forging cannons.
- October 16 – Russia approves the second Kamchatka expedition of Danish-born cartographer Vitus Bering, and the Admiralty orders him to sail east and try to claim uncharted lands in North America.
- November 29 – The magnitude 6.6 Irpinia earthquake causes 1,940 deaths in the former Kingdom of Naples.
- December 5 – 139 members of the Parliament of Paris, exiled by order of King Louis XV, secure their recall. 
- December 7 – The original Theatre Royal, Covent Garden, London (the modern-day Royal Opera House) is opened.
- December 19 – Benjamin Franklin, in the Pennsylvania Gazette, first advertises the publication of Poor Richard's Almanack, purportedly written by "Richard Saunders", a pen name used by Franklin.  The book goes on sale on December 28.  The annual publication will continue until 1758.
- Herman Boerhaave publishes the authorized edition of his Elementa chemiae, recognised as the first text on chemistry.
- The world's first lightship is moored at the Nore, in the Thames Estuary of England.
- This year's General Assembly of the Church of Scotland gives rise to the First Secession of 1733.
- January 13 – Borommarachathirat V becomes King of Siam (now Thailand) upon the death of King Sanphet IX.
- January 27 – George Frideric Handel's classic opera, Orlando is performed for the first time, making its debut at the King's Theatre in London.
- February 12 – British colonist James Oglethorpe founds Savannah, Georgia.
- March 21 – The Molasses Act is passed by British House of Commons, which reinforces the negative opinions of the British by American colonists. The Act then goes to the House of Lords, which consents to it on May 4 and it receives royal assent on May 17.
- March 25 – English replaces Latin and Law French as the official language of English and Scottish courts following the enforcement of the Proceedings in Courts of Justice Act 1730.
- April 6 –
- After British Prime Minister Robert Walpole's proposed excise tax bill results in rioting over the imposition of additional taxes and the use of government agents to collect them, Walpole informs the House of Commons that he will withdraw the legislation.
- Royal Colony of North Carolina Commissioners John Watson, Joshua Grainger, Michael Higgins and James Wimble begin selling lots for the town of New Carthage (which is later renamed and is now Wilmington, North Carolina), on the east side of the Cape Fear River.
- May 1 – The canton system is first introduced in Prussia.
- May 17 – The Molasses Act receives royal assent and begins to go into effect on June 24.
- May 29 – The right of Canadians to keep Indian slaves is upheld at Quebec.
- June 12 – In Berlin, Prince Frederick of Prussia, the 21-year-old heir to the throne reluctantly marries Duchess Elisabeth Christine of Brunswick-Bevern in order to avoid prosecution for desertion from the Prussian Army and to be guaranteed the throne. Despite the unhappy marriage Frederick and Elisabeth later reign as King and Queen Consort of Prussia.
- June 15 – The Danish West India Company buys the island of Saint Croix from France for 750,000 livres.
- July 15 – A hurricane off of the coast of the Florida Keys wrecks at least 17 Spanish ships.
- July 30 – The first Freemasons lodge opens in what will become the United States of America.
- August 19 – In Warsaw as Stanislas Leszczynski appears to be on the verge of being elected King of Poland, Russia, Austria and Saxony sign Löwenwolde's Treaty (named for Russian diplomat Karl Gustav von Löwenwolde), pledging to go to war to place Frederick Augustus, son of the late King Augustus II, on the throne.
- September 12 – Stanislas Leszczynski, who had been King of Poland from 1704 to 1709 until being driven from the throne by King Augustus II, is returned to office by the vote of the Sejm. Russia and Austria protest the election, since King Stanislaus is backed by France and Sweden.
- September 26 – The Treaty of Turin is signed in Turin as a secret agreement between King Louis XV of France and King Charles Emmanuel III of Sardinia.
- October 5 – The election of Augustus III, to succeed his father as King of Poland, sparks the War of the Polish Succession.
- October 10 – France declares war on Austria and Saxony .
- October 24 – The Battle of Kirkuk starts which will lead to the defeat of the Ottoman army under general Topal Osman Pasha.
- November 23 – The 1733 slave insurrection on St. John begins: Slaves from Akwamu rebel against their owners in the Danish West Indies.
- December 19 – Unsuccessful in capturing Baghdad from the Ottoman Empire, Persia's ruler Nader Shah signs the Treaty of Baghdad with the Ottoman Governor, Ahmad Khan Pasha, with the Turks and the Iranians agreeing to restore the boundary between the two empires to the lines before the 1732 Ottoman invasion of Iran.
- December 25 – The Molasses Act goes into full effect.
- January 8 – Salzburgers, Lutherans who were expelled by the Roman Catholic Bishop of Salzburg, Austria, in October 1731, set sail for the British Colony of Georgia, in America.
- February 16 – The Ostend Company, established in 1722 in the Austrian Netherlands (now Belgium) to compete for trade in the West Indies (the Caribbean islands) and the East Indies (south and southeast Asia), ceases business as part of the agreement by Austria in the Second Treaty of Vienna.
- March 12 – Salzburgers arrive at the mouth of the Savannah River, in the British Colony of Georgia.
- April 22 – Voting begins for the British House of Commons in some parliamentary constituencies. In that voting dates vary, the election continues until June 6.
- April 25 – Easter occurs on the latest possible date (the next time is in 1886).
- May 15 – Prince Charles of Spain (later King Charles III) becomes the new King of Naples and Sicily, five days after his arrival in Naples.
- May 25 – Spanish forces under the command of José Carrillo de Albornoz, 1st Duke of Montemar, defeat the Austrian forces, completing the conquest of the Kingdom of Naples at the Battle of Bitonto.
- May 27 – French and Swiss troops suppress the slave insurrection in the Danish West Indies on the island of Saint John (now part of the U.S. Virgin Islands) after six months and restore control of the plantations to the Danish owners. 
- June 6 – With the conclusion of the British general election, the Whigs, led by Prime Minister Robert Walpole, lose 85 seats but retain their majority.
- June 17 – French troops take Philippsburg, but Duke of Berwick is killed.
- June 21 – In Montreal, New France, a black slave known by the French name of Marie-Joseph Angélique is tortured then hanged by the French authorities for allegedly setting a fire that destroyed part of the city.
- June 30 – War of the Polish Succession: Russian troops take Gdańsk (German: Danzig), which had been besieged since February 1734, after the failure of a French expedition to relieve the city.
- July 18 – The Siege of the Austrian fortress of Philippsburg (near Karlsruhe, Germany) by the French Army, ends after eight weeks as its Austrian defenders surrender.
- August 6 – The armies of Spain and France, led by the Duke of Parma (and future King Charles III of Spain) storm the city of Gaeta in Naples, ending a four-month siege
- September 28 – Abdu'llah bin Ismail as-Samin is deposed after a 15-year reign as Sultan of Morocco.
- October 23 – Jamaica's Governor John Ayscough declares martial law to fight the slave rebellion that began in 1733, then drafts 600 men into the colonial army to march into the Blue Mountains. 
- October 31 – Chief Tomochichi of the Yamacraw band of the Muscogee Nation ends a successful four and a half month visit to Great Britain, along with Georgia Governor James Oglethorpe and other Yamacraw Indians, after having signed the cession of the area of modern day Savannah, Georgia to the Georgia Company. On June 16, he and the Muscogee delegation (Senauki, Toonahowi, Hillispilli, Umpichi, Apokutchi, Santachi and Stimaletchi) had been welcomed as a guest of King George II. The group departs on HMS Aldborough after completing the visit by the largest delegation of Native Americans since 1616. 
- November 5 – The Dzików Confederation is created in Poland.
- December 24 – A fire destroys the Royal Alcázar of Madrid, the residence of the Spanish royal family, along with more than 400 valuable paintings, 100 sculptures and thousands of documents.
- January 2 – Alexander Pope's poem Epistle to Dr Arbuthnot is published in London.
- January 8 – George Frideric Handel's opera Ariodante is premièred at the Royal Opera House in Covent Garden, London.
- February 3 – All 256 people on board the Dutch East India Company ships Vliegenthart and Anna Catherina die when the two ships sink in a gale off of the Netherlands coast. The wreckage of Vliegenthart remains undiscovered until 1981. 
- February 14 – The Order of St. Anna is established in Russia, in honor of the daughter of Peter the Great.
- March 10 – The Russian Empire and Persia sign the Treaty of Ganja, with Russia ceding territories in the Caucasus mountains to Persia, and the two rivals forming a defensive alliance against the Ottoman Empire.
- March 11 – Abraham Patras becomes the Governor-General of the Dutch East Indies (now Indonesia) upon the death of Dirck van Cloon.
- April 13 – Emperor Sakuramachi accedes to the throne of Japan.
- April 16 – Alcina, George Frideric Handel's Italian opera, premieres at the Royal Opera House in Covent Garden, London.
- May 22 – George Hadley publishes the first explanation of the trade winds.
- June 24 – Effective date of Great Britain's Witchcraft Act of 1735, which criminalized claimants accusing people of practising witchcraft, or of possessing magical powers.
- July 11 – Pluto (not known at this time) enters a fourteen-year period inside the orbit of Neptune, which will not recur until 1979.
- August 14 – Freedom of the press: The New York Weekly Journal writer John Peter Zenger is acquitted of seditious libel against the royal governor of New York, on the basis that what he published was true.
- September 4 – Al-Husayn I ibn Ali, the first Bey of Tunis (now Tunisia) is defeated at the Battle of Smindja by Abu l-Hasan Ali I with the help of Ibrahim ben Ramdan, the Dey of Algiers.
- September 14 – The Kingdom of France approves the issue of "card money" in the total amount of 200,000 livres to serve as currency in its Louisiana territory in America.
- September 22 – Sir Robert Walpole, the Prime Minister of Great Britain, becomes the first British premier to move into London's 10 Downing Street.
- October 3 – An agreement between the European powers brings a ceasefire in the War of the Polish Succession, one week short of the second anniversary of the war. With France and Spain on the side of the reigning monarch, Stanisław Leszczyński, and Prussia, Russia, and Austria supporting Augustus III, a preliminary peace is signed allowing Stanislaw to reign in Warsaw and Augustus to reign in Krakow, and is ratified in 1738.
- October 18 – In China, Qianlong succeeds his father, Yongzheng as Emperor and begins a 60-year-long reign within the Qing Dynasty.
- November 25 – The largest bell in the world, the 22 feet (6.7 m) diameter Tsar Kolokol, is successfully cast in Moscow within the Kremlin. 
- November 30 – The Netherlands becomes the first government to announce a prohibition against citizens joining the Freemasons. 
- December 19 – At the age of 8 years old, Prince Luis of Spain becomes the youngest Roman Catholic Cardinal in history, after being named by Pope Clement XII.
- Linnaeus publishes his Systema Naturae.
- Russo-Turkish War, 1735-1739: Russian forces fail to occupy the Crimea, due to rasputitsa.
- A shipbuilding industry begins in Mumbai.
- Leonhard Euler solves the Basel problem, first posed by Pietro Mengoli in 1644, and the Seven Bridges of Königsberg problem.
- The King's Highway (Charleston to Boston) is completed.
- Quebec: Construction begins on the Chemin du roy between Quebec and Montreal.
- Augusta, Georgia, is founded.
- Cobalt is discovered and isolated by Georg Brandt.
- The first successful appendectomy is performed, by French surgeon Claudius Aymand in London.
- January 12 – George Hamilton, 1st Earl of Orkney, becomes the first Field Marshal of Great Britain.
- January 23 – The Civil Code of 1734 is passed in Sweden.
- January 26 – Stanislaus I of Poland abdicates his throne.
- February 12 – Francis I, Holy Roman Emperor marries Maria Theresa of Austria, ruler of the Habsburg Empire.
- March 8 – Nader Shah, founder of the Afsharid Dynasty, is crowned Shah of Iran on a date selected by court astrologers. 
- March 31 – Bellevue Hospital is founded in New York.
- April 14 – The Porteous Riots erupt in Edinburgh, after the execution of smuggler Andrew Wilson, when town guard Captain John Porteous orders his men to fire at the crowd. Porteous is arrested later.
- April 14 – German adventurer Theodor Stephan Freiherr von Neuhoff is crowned King Theodore of Corsica, 25 days after his arrival on the island on March 20. His reign ends on November 5 when he flees Corsica.
- April 19 – A fire in Stony Stratford, England consumes 53 houses.
- April 25 – Easter occurs on the latest possible date (the next time is in 1886).
- April – The Genbun era begins in Japan. The era of Kyōhō Reforms ends.
- May 8 – Frederick, Prince of Wales, marries Princess Augusta of Saxe-Gotha.
- May 22 – King George II of Great Britain departs for Europe as part of his duties as Elector of Hanover; his wife, Caroline, Queen Consort rules on his behalf as the Regent for the last time until his return on January 14. 
- May 26 – Battle of Ackia: British and Chickasaw Native Americans defeat French troops.
- June 8 – Leonhard Euler writes to James Stirling, describing the Euler–Maclaurin formula, providing a connection between integrals and sums.
- June 19 – A French Academy of Sciences expedition, led by Pierre Louis Maupertuis, with Anders Celsius, begins work on measuring a meridian arc in Meänmaa, Finland.
- July 1 – Russo-Turkish War (1735–39): Russian forces under Peter Lacy storm the Ottoman fortress of Azov. 
- August 12 – A fire in Saint Petersburg, capital of the Russian Empire, destroys 2,000 buildings, the city's post office, and several palaces.
- September 7 – An Edinburgh crowd drags John Porteous out of his cell in Tolbooth Prison, and lynches him.
- September 29 – The Gin Act 1736 goes into effect, placing a steep tax on the sale of gin and license requirements for its sale, with the intent of reducing consumption of the liquor in Britain. Widely ignored, the Act is repealed in 1743. 
- October 3 – French scientist Charles Marie de La Condamine and a team of surveyors begin the first measurements at the Equator to determine the exact meridian arc measurement of distance between points separated by one degree of longitude in order to make a precise calculation of the Earth's circumference.  The initial measurements, made in what is now Ecuador, last until November 3.
- November 5 – King Theodore of Corsica flees the island after a reign of seven months and the kingdom reverts to French control. 
- November 13 – Word of the discovery of silver, south of what is now the U.S.-Mexican border, reaches Sonora Governor Juan Bautista Anza and soon leads to prospectors coming to Nogales to find more silver.  Late in October, a Yaqui Indian prospector, Antonio Siraumea, had discovered large slabs of silver ("Las planchas de plata"), and at the Estancia Arizona, a ranch owned by Captain Bernardo de Urrea. The region, and later the U.S. territory, and state of Arizona are named for Urrea's ranch.
- December 7 – Benjamin Franklin builds the first volunteer fire company in Philadelphia.
- December 26 – Andrew Michael Ramsay gives an oration, in which he relates the heritage and internationalism of Freemasonry to that of the Crusades.
- Neustrelitz becomes the capital of Mecklenburg-Strelitz.
- Bushehr is founded in Persia.
- The Belgrade Fortress is completed.
- One of the earliest records of use of a bathing machine is made at Scarborough, England.
- Charles Marie de La Condamine, with François Fresneau Gataudière, makes the first scientific observations of rubber, in Ecuador.
- Leonhard Euler produces the first published proof of Fermat's "little theorem".
- Sir Isaac Newton's Method of Fluxions (1671), describing his method of differential calculus, is first published (posthumously) and Thomas Bayes publishes a defense of its logical foundations (anonymously).
- Muhammad ibn Abd al-Wahhab writes the Kitab at-tawhidt, marking the beginning of Wahhabism.
- The Haidamakas raid the shtetl of Pavoloch, killing 35.
- January 5 – Spain and the Holy Roman Empire sign instruments of cession at Pontremoli in the Grand Duchy of Tuscany in Italy, with the Empire receiving control of Tuscany and the Grand Duchy of Parma and Piacenza, in return for Don Carlos of Spain being recognized as King of Naples and King of Sicily. 
- January 9 – The Empires of Austria and Russia enter into a secret military alliance that leads to Austria's disastrous entry into the Russo-Turkish War. 
- January 18 – In Manila, a peace treaty is signed between Spain's Governor-General of the Philippines, Fernándo Valdés y Tamon, and the Sultan Azim ud-Din I of Sulu, recognizing Azim's authority over the islands of the Sulu Archipelago.  
- February 16 – George Frideric Handel's opera Giustino is performed for the first time, premiering in London at the Theatre Royal (now the Royal Opera House).
- February 20 – France's Foreign Minister, Germain Louis Chauvelin, is fired by King Louis XV's Chief Minister, Cardinal André-Hercule de Fleury
- February 27 – French scientists Henri-Louis Duhamel du Monceau and Georges-Louis Leclerc de Buffon publish the first study of correlating past weather conditions with an examination of tree rings), "On the cause of the eccentricity of the woody layers which one perceives when one cuts horizontally the trunk of a tree" (De la cause de l'excentricité des couches ligneuses qu'on apperçoit quand on coupe horisontalement le tronc d'un arbre)
- March 16 – In Paris, representatives of Spain and Portugal sign an armistice bringing and end to the Spanish–Portuguese War over the area now occupied by the nation of Uruguay and the area now occupied by the state of Rio Grande do Sul in Brazil. The news does not reach the fighting parties until five months later. 
- March 28 – The Battle of Delhi takes place between the Maratha Empire and the Mughals.
- April 5 –French Jesuit priest Jean-François Régis is canonized as Saint Regis by the Roman Catholic Church under the reign of Pope Clement XII.
- April 22 –
- In Afghanistan, Persian shah Nader Shah begins the 11-month Siege of Kandahar against the Pashtun Emir of Afghanistan, Hussain Hotak.  The surviving Afghanis surrender on March 24. p613
- Lots are first advertised for sale in the new town of Richmond, Virginia, by the placement of a notice by William Byrd in the Virginia Gazette. According to the paper, "... on the North Side of James River, near the Uppermost Landing, and a little below the Falls, is lately laid off by Major Mayo, a Town, called Richmond, with Streets 65 Feet wide, in a pleasant and healthy Situation, and well supply'd with Springs of good Water. It lies near the Publick Warehouse at Shoccoe's, and in the midst of great Quantities of Grain, and all kind of Provisions. The Lots will be granted in Fee Simple, on Condition only of building a House in Three Years Time, of 24 by 16 Feet, fronting within 5 Feet of the Street. The Lots to be rated according to the Convenience of their Situation, and to be sold after this April General Court, by me, William Byrd." 
- May 28 – The planet Venus passes in front of Mercury. The event is witnessed during the evening hours, by the amateur astronomer John Bevis, at the Royal Greenwich Observatory. As of 2006, it is still the only such planet/planet occultation that has been directly observed.
- June 21 – In Britain, the Theatrical Licensing Act requires plays to be submitted to the Lord Chamberlain for censorship.
- June 30 – Russo-Turkish War, 1735-1739: Russian forces under Field Marshal Munnich storm the Ottoman fortress of Ochakov, and take prisoner 4,000 Turks.
- July 12 – Austria enters the Russo-Turkish War as an ally of Russia against the Ottoman Empire. 
- July 17 – The British ship Catherine founders in a storm off of Nova Scotia's Cape Sable Island during its voyage from Ireland to Boston, killing 98 of the 201 people on board.
- August 4 – Austria's army is defeated by the Ottoman Army and Bosnian defenders in the Battle of Banja Luka.
- August 15 – The Portuguese frigate Nossa Senhora da Boa Viagem arrives at Maldonado (now in Uruguay) as Captain Duarte Pereira brings the news that the Spanish–Portuguese War ended by an agreement signed on March 16. 
- September 1 – The oldest existing English language newspaper in the world, The News Letter, is founded in Belfast, Ireland.
- September 20 – Runner Edward Marshall completes his journey in the Walking Purchase, forcing the cession of 1,200,000 acres (4,900 km2) of Lenape-Delaware tribal land to the Pennsylvania Colony.
- October 7 – At least 300,000 people are killed when a tropical cyclone strikes the Bay of Bengal in India and modern-day Bangladesh. The storm sends 12 metres (39 ft) high waves over the Sundarbans delta, and overflows the Hooghly River. 
- October 11 – The first national stage in Sweden opens, when Carl Gyllenborg's play Den svenska sprätthöken is performed in the Swedish language, by the first native actors, on the stage of Bollhuset in Stockholm. 
- October 16 – An earthquake with an estimated magnitude of 9.3 occurs off the shore of Russia's Kamchatka Peninsula. Tsunamis up to 60 metres (200 ft) high follow in the Pacific ocean.
- November 4 – The Teatro di San Carlo, the oldest working opera house in Europe, is inaugurated in Naples, Italy.
- December 24 – General Baji Rao I of the Maratha Empire in India defeats the armies of the rulers of Hyderabad, Oudh, Bhopal and Jaipur in the Battle of Bhopal.
- Benjamin Franklin creates the Philadelphia Police Force – the first city-paid force in 1737.
- The Georg August University of Göttingen is founded.
- The direct male line of the Medici family becomes extinct, with the death of Gian Gastone de' Medici, Grand Duke of Tuscany.
- Richmond, Virginia is founded.
- Our Lady of Guadalupe is designated the patron saint of Mexico City.
- Lancaster County Prison, Lancaster, Pennsylvania is first constructed, in response to the seven preceding violent years of the ongoing Cresap's War, in the Maryland-Pennsylvania boundary dispute and war.
- January 1 – At least 664 African slaves drown when the Dutch West Indies Company slave ship Leusden capsizes and sinks in the Maroni River during its arrival in Surinam. The Dutch crew escapes and leaves the slaves locked below decks to die.
- January 3 – George Frideric Handel's opera Faramondo is given its first performance.
- January 7 – After the Maratha Empire of India wins the Battle of Bhopal over the Jaipur State, Jaipur cedes the Malwa territory to the Maratha in a treaty signed at Doraha.
- February 4 – Court Jew Joseph Süß Oppenheimer is executed in Württemberg.
- February 11 – Jacques de Vaucanson stages the first demonstration of an early automaton, The Flute Player at the Hotel de Longueville in Paris, and continues to display it until March 30.
- February 20 – Swedish Levant Company founded.
- March 28 – The British House of Commons votes, 257 to 209, for a resolution in favor of a war with Spain, clearing the way for the 1739 War of Jenkins' Ear after years of lobbying my mariner Robert Jenkins. Basil Williams, The Life of Wiliam Pitt Earl of Chatham (Longmans, Green, and Co., 1913), reprinted by Routledge, 2018
- March/April – Battle of the Dindar River: Emperor Iyasu II of Ethiopia is defeated by the Funj.
- April 15 – Serse, an Italian opera by George Frideric Handel, premieres in London.
- April 18 – Spain's Royal Academy of History (Real Academia de la Historia) is established by decree of King Philip V of Spain.
- April 28 – Pope Clement XII issues the papal bull In eminenti apostolatus, prohibiting Roman Catholics from being members of Masonic socieities.
- May 24 – John Wesley experiences a spiritual rebirth at a Moravian Church meeting in Aldersgate, in the City of London, essentially launching the Methodist movement; the day is celebrated annually by Methodists as Aldersgate Day (his younger brother Charles had a similar experience three days earlier).
- May 25 – The military phase of Cresap's War between the British North American Provinces of Maryland and Pennsylvania is ended when King George II of Great Britain negotiates a cease-fire.
- June 24 – British inventor Lewis Paul receives a patent for his invention of the "roller spinning", which will revolutionize the textile industry.
- June 27 – The Spanish Empire's Council of the Indies votes, 6 to 4, to re-establish the Viceroyalty of New Granada, incorporating modern-day Colombia, Ecuador, Venezuela and Panama. King Philip V issues the order on August 20, 1738.
- July 1 – William Champion is granted a patent for his process of extracting zinc from other materials in a furnace.
- July 10 – Thomas Pellow of Cornwall finally escapes captivity, 23 years after he had been captured by Barbary pirates and held as a slave in Morocco. He arrives in British territory when the ship he is on sails into Gibraltar Bay on July 21, and later recounts his story in the book The Adventures of Thomas Pellow, of Penryn, Mariner: Three and Twenty Years in Captivity Among the Moors.
- August 10 – Russo-Turkish War (1735–1739): The Russian army begins its attempt to cross the Dniester River and fails after three weeks; they are later decimated by plague.
- September 18 – Samuel Johnson composes his first solemn prayer (published 1785).
- October 22 – The excavation of Herculaneum, a Roman city buried by Vesuvius in AD 79, begins near the Italian city of Resina on orders from King Charles VII of Spain to his engineer, Rocque Joaquin de Alcubierre.
- November 18 – The Treaty of Vienna is ratified, ending the War of the Polish Succession. Under the terms of the treaty, Stanisław Leszczyński receives Lorraine, in exchange for renouncing the Polish throne.
- December 27 – After setting off from Rotterdam in August with 240 immigrants to America, the British ship Princess Augusta is wrecked near Block Island off of the coast of the colony of Rhode Island. During the voyage, 200 passengers and seven crew died from illness spread by contaminated water. Another 20 die after the crew leaves rows to shore. The wreck later becomes the subject of the legend of the "Palatine Light" ghost ship and of John Greenleaf Whittier's 1867 poem "The Palatine".
- Specific date unknown: Carl Philipp Emanuel Bach, having completed a law degree, is hired as a court musician by Crown Prince Frederick of Prussia, the future Frederick the Great (Bach will remain in Frederick's service until 1768).
- China's Qing government announces that all western businessmen have to use the Cohong in Guangzhou to trade.
- Pierre Louis Maupertuis publishes Sur la figure de la terre, which confirms Newton's view that the earth is an oblate spheroid, slightly flattened at the poles.
- Black Forest clockmaker Franz Ketterer produces one of the earliest cuckoo clocks.
- Holy Royal Arch is founded.
- Rémy Martin is granted exclusive permission by King Louis XV of France to plant new vineyards, for impressing him with the quality of his cognac.
- January 1 – Bouvet Island is discovered by French explorer Jean-Baptiste Charles Bouvet de Lozier, in the South Atlantic Ocean.
- February 24 – Battle of Karnal: The army of Iranian ruler Nader Shah defeats the forces of the Mughal emperor of India, Muhammad Shah.
- March 20 – Nader Shah occupies Delhi, India and sacks the city, stealing the jewels of the Peacock Throne, including the Koh-i-Noor.
- April 7 – English highwayman Dick Turpin is executed by hanging for horse theft.
- May 12 – John Wesley lays the foundation stone of the New Room, Bristol in England, the world's first Methodist meeting house.
- June 2 – The Royal Swedish Academy of Sciences is founded in Stockholm, Sweden.
- July 9 – The first group purporting to represent an all-England cricket team, consisting of 11 players from various parts of England, comes to Kent and loses to the renowned Kent team, led by Lord John Sackville. 
- July 12 – The British East India Company signs a treaty with the Maratha Empire to gain the right of free trade within the territory. 
- July 22 – the Ottoman Empire retakes Belgrade from Austria's Habsburg Monarchy after winning the Battle of Grocka. 
- August 20 – The Viceroyalty of New Granada, incorporating modern-day Colombia, Ecuador, and Venezuela is re-established by the royal cedula of King Philip V of Spain, 16 years after it had been dissolved, and adds the territory of Panama as well. 
- September 9 – The Stono Rebellion, a slave rebellion, erupts near Charleston, South Carolina.
- September 18 – The Treaty of Belgrade brings the Austro-Russian–Turkish War (1735–39) to an end.
- October 3 – The Treaty of Niš is signed.
- October 17 – The Foundling Hospital is created in London by royal charter.
- October 23 – War of Jenkins' Ear: Great Britain declares war on Spain.
- November 20–22 – War of Jenkins' Ear – Battle of Porto Bello: British marine forces capture the Panamanian silver exporting town of Portobelo from the Spanish.
- December 30– Months of unseasonably cold weather begin in Ireland, precipitating the Irish Famine of 1740, known as Bliain an Áir ("The Year of Slaughter"). A January 5 dispatch from Dublin to the Stamford Mercury says "Since last Wednesday we have had the most violent cold Weather that was ever known in this Kingdom; hard Frost began that evening, which has continued ever since with a very stormy Wind at South-East."  At least 13% of Ireland's population dies of starvation in the year that follows. 
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