|Centuries:||15th century – 16th century – 17th century|
|Decades:||1500s 1510s 1520s – 1530s – 1540s 1550s 1560s|
|Years:||1532 1533 1534 – 1535 – 1536 1537 1538|
- January 18 – Lima, Peru founded by Francisco Pizarro
- April – Jacques Cartier discovers the Iroquois city of Stadacona, Canada (now Quebec) and in May, the even greater Huron city of Hochelaga
- June 24 – The Anabaptist state of Münster (see Münster Rebellion) is conquered and disbanded.
- May 19 – French explorer Jacques Cartier sets sail for his second voyage to North America with 3 ships, 110 men, and Chief Donnacona's 2 sons (who Cartier kidnapped during his first voyage).
- October 2 – Jacques Cartier discovers Montreal, Quebec.
- October 4 – The first complete English-language Bible is printed, with translations by William Tyndale and Miles Coverdale.
- Combined Swedish and Danish fleets defeat the Hanseatic navy.
- Manco II appointed puppet Inca Emperor by Spanish Conquistadors
- Second unsuccessful attempt by Spanish forces to conquer Yucatán
- Carlos Quinto conquers Tunis
- Anabaptist rebellion in some cities in the Netherlands, including a famous incident of seven men and five woman walking nude in the streets of Amsterdam.
- The Charterhouse London is closed, as part of Henry VIII's Dissolution of the Monasteries.