|Covid-19|January – Bigod's Rebellion, an uprising by Roman Catholics against Henry VIII of England
January 6 – Alessandro de' Medici, Duke of Florence is assassinated.
March – Diego de Almagro successfully charges Manco Inca's siege of Cuzco, thereby saving his antagonists, the Pizarro brothers.
March 12 – Recife is founded by the Portuguese in Brazil.
April 1 - the definite end of Catholicism in Norway. Archbishop Olav Engelbrektsson flees from Nidaros (Trondheim) to Lier, Belgium.
June 2 – Pope Paul III publishes the encyclical Sublimis Deus, which declares the natives of the New World to be rational beings with souls who must not be enslaved or robbed.
August 15 – Asunción is founded by Juan de Salazar de Espinosa.
August 25 – The Honourable Artillery Company, the oldest surviving regiment in the British Army, and the second most senior, is formed.
August-September – The Ottomans fail to capture Corfu.
Manco Cápac establishes the independent Neo-Inca State at Vilcabamba, Peru.
The Spaniards bring the potato to Europe.
Kiritimati (Acea or "Christmas Island") is discovered by the Spanish expedition of Hernando de Grijalva.
The island of Paros is conquered by the Ottoman Empire
Religious buildings are dissolved by Henry VIII of England, including
Castle Acre Priory,
Valle Crucis Abbey, and
Bisham Priory (Bisham Abbey being founded in its place).
Bangalore is first mentioned.
January 1 – Jan Krzysztof Tarnowski, Polish noble (d. 1567)
January 16 – Albrecht VII, Count of Schwarzburg-Rudolstadt (d. 1605)
January 21 – Antonio Maria Salviati, Catholic cardinal (d. 1602)
February 26 – Christopher II, Margrave of Baden-Rodemachern (d. 1575)
March 4 – Longqing Emperor, Emperor of China (d. 1572)
May 18 – Guido Luca Ferrero, Roman Catholic cardinal (d. 1585)
May 20 – Hieronymus Fabricius, Italian anatomist (d. 1619)
May 27 – Louis IV, Landgrave of Hesse-Marburg, son of Landgrave Philip I (d. 1604)
May 28 – Ismail II, Shah of Persia (d. 1577)
June 3 – João Manuel, Prince of Portugal, Portuguese prince (d. 1554)
July 20 – Arnaud d'Ossat, French diplomat and writer (d. 1604)
July 29 – Pedro Téllez-Girón, 1st Duke of Osuna, Spanish duke (d. 1590)
July 30 – Christopher, Duke of Mecklenburg and administrator of Ratzeburg (d. 1592)
August 9 – Francesco Barozzi, Italian mathematician (d. 1604)
August 15 – Shimazu Toshihisa, Samurai (d. 1592)
King Edward VI of England, son of King Henry VIII of England and Queen Jane Seymour (d. 1553)
Lady Jane Grey, claimant to the throne of England (d. 1554)
December 5 – Ashikaga Yoshiaki, Japanese shogun (d. 1597)
December 20 – King John III of Sweden (d. 1592)
December 24 – Willem IV van den Bergh (d. 1586)
December 26 – Albert, Count of Nassau-Weilburg (d. 1593)
Jane Lumley, English translator (d. 1578)
Fadrique Álvarez de Toledo, 4th Duke of Alba, Spanish military leader (d. 1583)
Shimizu Muneharu, Japanese military commander (d. 1582)
John Almond, Cistercian monk (d. 1585)
Alessandro de' Medici, Duke of Florence (b. 1510)
Baldassare Peruzzi, Italian architect and painter (b. 1481)
January 12 – Lorenzo di Credi, Florentine painter and sculptor (b. 1459)
February 3 – Thomas FitzGerald, 10th Earl of Kildare (executed) (b. 1513)
Otto von Pack, German conspirator (b. c. 1480)
Saint Gerolamo Emiliani, Italian humanitarian (b. 1481)
June 23 – Pedro de Mendoza, Spanish conquistador (b. 1487)
June 29 – Henry Percy, 6th Earl of Northumberland (b. 1502)
July 7 – Madeleine of Valois, queen of James V of Scotland (b. 1520)
July 14 – Robert Aske (executed) (b. 1500)
September 4 – Johann Dietenberger, German theologian (b. c. 1475)
October 9 – Pavle Bakić, last Serb Despot and medieval Serb monarch
October 24 – Jane Seymour, Third Queen of Henry VIII of England (complications of childbirth) (b. c. 1508)
date unknown – John Kite, Archbishop of Armagh and Bishop of Carlisle
probable – Thomas Murner, German satirist (b. 1475)
Year 1537 (MDXXXVII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar.