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.
- March 12 – John Glas is deposed from the Church of Scotland; the Glasite sect forms around him.
- April 8 – Shearith Israel, the first synagogue in New York City, is dedicated.
- 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.
- May – At the urging of Sir William Gooch, the Virginia House of Burgesses passes the Tobacco Inspection Act of 1730 to regulate the quality of Virginian tobacco, and establish inspection warehouses near plantations in the Tidewater region. 
- The establishment of Wright's Ferry under the authority of the Province of Pennsylvania triggers 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.
- July 8 – An earthquake affects Valparaiso, in the Viceroyalty of Peru.
- July 12 – Pope Clement XII succeeds Pope Benedict XIII, as the 246th pope.
- 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 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.
- 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 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.
- April – British trader Robert Jenkins has his ear cut off by Spanish coast guards in Cuba, casus belli for the War of Jenkins' Ear in 1739.
- 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.
- 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. 
- 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.
- June 9 – James Oglethorpe is granted a royal charter for the colony of Georgia.
- August – 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.
- September 16 – The magnitude 5.8 Montreal earthquake occurs in Montreal, Quebec, Canada.
- December 7 – The original Theatre Royal, Covent Garden, London (the modern-day Royal Opera House) is opened.
- December – 139 members of the Parlement of Paris, exiled by order of King Louis XV, secure their recall.
- Herman Boerhaave publishes the authorized edition of his Elementa chemiae, recognised as the first text on chemistry.
- The Republic of Genoa regains Corsica.
- 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.
- February 12 – British colonist James Oglethorpe founds Savannah, Georgia.
- March – The Molasses Act is passed by the Parliament of Great Britain, which reinforces the negative opinions of the British by American colonists.
- April – Royal Colony of North Carolina Commissioners John Watson, Joshua Grainger, Michael Higgins and James Wimble plan the town of New Carthage (which will eventually become Wilmington, North Carolina, on the east side of the Cape Fear River).
- May 1 – The canton system is first introduced in Prussia.
- May 29 – The right of Canadians to keep Indian slaves is upheld at Quebec.
- July 30 – The first Freemasons lodge opens in what will become the United States of America.
- October 5 – The election of Augustus III, to succeed his father as King of Poland, sparks the War of the Polish Succession.
- 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.
- 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.
- March 12 – Salzburgers arrive at the mouth of the Savannah River, in the British Colony of Georgia.
- 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.
- 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 14 – The Order of St. Anna is established in Russia, in honour of the daughter of Peter the Great.
- 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.
- October – War of the Polish Succession: A preliminary peace, ratified in 1738, is concluded.
- October 18 – The Qianlong Emperor succeeds his father, the Yongzheng Emperor, and begins a 60-year-long reign of the Qing Dynasty.
- 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 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.
- April – The Genbun era begins in Japan. The era of Kyōhō Reforms ends.
- March 8 – Nader Shah, founder of the Afsharid Dynasty, is crowned Shah of Iran.
- March 31 – Bellevue Hospital was founded.
- 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.
- May 8 – Frederick, Prince of Wales, marries Princess Augusta of Saxe-Gotha.
- 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 – Russo-Turkish War (1735–39): Russian forces under Peter Lacy storm the Ottoman fortress of Azov.
- August 12 – A fire in St. 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.
- 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.
- George Hamilton, 1st Earl of Orkney, becomes the first Field Marshal of Great Britain.
- A fire in the Russian city of Saint Petersburg burns 2,000 houses.
- A fire in Stony Stratford, England consumes 53 houses.
- 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.
- March 28 – The Battle of Delhi takes place between the Maratha Empire and the Mughals.
- 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 – Austria enters the Russo-Turkish War.
- 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 – The first national stage in Sweden opens, when the play Den svenska sprätthöken is performed in the native language, by the first native actors, on the stage of Bollhuset in Stockholm.
- October 7 – A tropical cyclone strikes Bengal, India, killing approximately 300,000.
- 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.
- Tony Brian Attenborough 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.
- 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/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.
- 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.
- 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.
- 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.
- 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.
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