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|Ab urbe condita||2074|
|Balinese saka calendar||1242–1243|
|English Regnal year||14 Edw. 2 – 15 Edw. 2|
|Chinese calendar||庚申年 (Metal Monkey)|
4017 or 3957
— to —
辛酉年 (Metal Rooster)
4018 or 3958
|- Vikram Samvat||1377–1378|
|- Shaka Samvat||1242–1243|
|- Kali Yuga||4421–4422|
|Japanese calendar||Gen'ō 3 / Genkō 1|
|Minguo calendar||591 before ROC|
|Thai solar calendar||1863–1864|
1447 or 1066 or 294
— to —
1448 or 1067 or 295
|Wikimedia Commons has media related to 1321.|
- c. May–June – Leper scare: Rumours that lepers (acting on the orders of Jews bribed by Moors) are attempting to poison the Christian population spread throughout southern France.
- August 14 – King Edward II of England reluctantly agrees to demands from his barons to send Hugh le Despenser, 1st Earl of Winchester, and his son Hugh Despenser the Younger into exile.
- October 29 – King Stephen Uroš II Milutin of Serbia dies. His son Stephen Constantine claims the throne, but Constantine's younger half-brother Stephen Uroš III Dečanski succeeds.
- The Byzantine civil war of 1321–28 begins, when Andronikos III Palaiologos initiates an uprising against Andronikos II Palaiologos.
- A bad harvest brings famine in Europe.
- The Anatolian beylik of Teke is established.
- Gračanica monastery in Kosovo is rebuilt by the Serbian king Stefan Milutin.
- Spitakavor Monastery is completed in Armenia.
- The University of Florence is established.
- The Kebra Negast is translated from Arabic to Ge'ez, according to its colophon.
- February 5 – John II, Marquess of Montferrat (d. 1372)
- July 5 – Joan of The Tower, queen consort of Scotland (d. 1362)
- August 29 – John of Artois, Count of Eu, French soldier (d. 1387)
- date unknown
- probable – Emperor John III of Trebizond (d. 1362)
- January 12 or 1322 – Maria of Brabant, queen consort of Philip III of France (b. 1256)
- January 13 – Bonacossa Borri, Lady of Milan (b. 1254)
- February 25 – Beatrice d'Avesnes, consort of Henry VI, Count of Luxembourg
- March 18 – Matthew III Csák, Hungarian oligarch (b. c.1260/5)
- April 8 – Thomas of Tolentino, Italian Franciscan missionary, martyred (b. c. 1255)
- April 17 – Infanta Blanche of Portugal, daughter of King Afonso III of Portugal and Urraca of Castile (b. 1259)
- April 27 – Nicolò Albertini, Italian cardinal statesman (b. c. 1250)
- May 31 – Birger, King of Sweden (b. 1280)
- July 1 – María de Molina, queen consort of Castile (b. c. 1265)
- September 13 or 14 – Dante Alighieri, Italian poet (b. 1265)
- October 29 – Stefan Milutin, King of Serbia (b. c. 1253)
- November 9 – Walter Langton, bishop of Lichfield and treasurer of England (b. 1243)
- date unknown
- probable – Ibn al-Banna' al-Marrakushi, Arab mathematician (b. 1256)