1513

January–June

• March 9 - Pope Leo X, the layman Giovanni di Lorenzo de' Medici, succeeds Pope Julius II, as the 217th pope, despite a strong challenge by Hungarian cardinal Tamás Bakócz.
• March 27 - Juan Ponce de León becomes the first European definitely known to sight Florida, mistaking it for another island.
• April 2 - Juan Ponce de León and his expedition become the first Europeans known to visit Florida, landing somewhere on the east coast.
• May - Portuguese explorer Jorge Álvares lands on Lintin Island, in the Pearl River estuary.
• June 6 - Italian Wars - Battle of Novara: Swiss mercenaries defeat the French under Louis II de la Trémoille, forcing the French to abandon Milan. Duke Massimiliano Sforza is restored.

  July–December

• July 22 - Christian II becomes King of Denmark and Norway.
• August 16 - Battle of Dubica : Croatian troops under Petar Berislavić, Ban of Croatia, defeat an Ottoman army under Sanjak-bey Junuz-aga
• August 16 - Battle of the Spurs : English and allied troops under Henry VIII defeat French cavalry under Marshal La Palice.
• August 22 - Thérouanne is captured by Henry VIII of England.
• September - The dispute between Johann Reuchlin and Johannes Pfefferkorn relative to the Talmud and other Jewish books, is referred to Pope Leo X.
• September 9 - Battle of Flodden: King James IV of Scotland is defeated and killed by an English army under Thomas Howard, Earl of Surrey. James's son, the Duke of Rothesay, becomes James V, King of Scots.
• September 25 - Vasco Núñez de Balboa, "silent upon a peak in Darién", first sees what will become known as the Pacific Ocean.
• October 7 - Battle of La Motta : Spanish troops under Ramón de Cardona and Fernando d'Avalos decisively defeat those of the Republic of Venice under Bartolomeo d'Alviano on Venetian territory.
• December
• * Louis XII of France makes peace with the Pope and Spain.
• * A major landslide occurs near Bellinzona.

  Undated

• Appenzell becomes a member of the Swiss Confederacy.
• Niccolò Machiavelli is banished from Florence by the House of Medici, and writes The Prince.
• Leo Africanus visits Timbuktu, second city of the Songhai Empire.
• Paracelsus begins studying at Ferrara University.