|Centuries:||16th century – 17th century – 18th century|
|Decades:||1650s 1660s 1670s – 1680s – 1690s 1700s 1710s|
|Years:||1681 1682 1683 – 1684 – 1685 1686 1687|
|Ab urbe condita||2437|
|Balinese saka calendar||1605–1606|
|English Regnal year||35 Cha. 2 – 36 Cha. 2|
|Chinese calendar||癸亥年 (Water Pig)|
4380 or 4320
— to —
甲子年 (Wood Rat)
4381 or 4321
|- Vikram Samvat||1740–1741|
|- Shaka Samvat||1605–1606|
|- Kali Yuga||4784–4785|
|Japanese calendar||Tenna 4 / Jōkyō 1|
|Julian calendar||Gregorian minus 10 days|
|Minguo calendar||228 before ROC|
|Thai solar calendar||2226–2227|
1810 or 1429 or 657
— to —
1811 or 1430 or 658
- July 24 – René-Robert Cavelier, Sieur de La Salle sails from France, again, with a large expedition designed to establish a French colony on the Gulf of Mexico, at the mouth of the Mississippi River.
- October 7 – Japanese Chief Minister Hotta Masatoshi is assassinated, leaving Shogun Tsunayoshi without any adequate advisors, leading him to issue impractical edicts and create hardships for the Japanese people.
- December 10 – Isaac Newton's derivation of Kepler's laws from his theory of gravity, contained in the paper De motu corporum in gyrum, is read to the Royal Society by Edmund Halley.
- France under Louis XIV makes Truce of Ratisbon separately with the Holy Roman Empire (Habsburg) and Spain.
- Pope Innocent XI forms a Holy League with the Habsburg Empire, Venice and Poland to liberate Europe from the Ottoman Turkish rule.
- The Japanese poet Saikaku composes 23,500 verses in 24 hours at the Sumiyoshi Shrine at Osaka; the scribes cannot keep pace with his dictation and just count the verses.
- The British East India Company receives Chinese permission to build a trading station at Canton. Tea sells in Europe for less than a shilling a pound, but the import duty of 5 shillings makes it too expensive for most English people to afford.
- Smuggled tea is drunk much more than legally imported tea.
- England has its coldest winter in living memory; the River Thames and the sea as far as 2 miles out from land freezes over.
- John Bunyan writes The Pilgrim's Progress Part 2.
- The Chipperfield's Circus dynasty begins when James Chipperfield introduces performing animals to England at the River Thames frost fairs on the Thames in London.
- January 1 – Arnold Drakenborch, Dutch classical scholar (died 1748)
- January 14 – Jean-Baptiste van Loo, French painter (died 1745)
- February 24 – Matthias Braun, Czech sculptor (died 1738)
- March 15 – Francesco Durante, Italian composer (died 1755)
- March 19 – Jean Astruc, French physician and scholar (died 1766)
- April 15 – Catherine I of Russia (died 1727)
- June 22 – Francesco Manfredini, Italian composer (died 1762)
- September 18 – Johann Gottfried Walther, German music theorist, organist, and composer (died 1748)
- October 10 – Antoine Watteau, French painter (died 1721)
- October 26 – Kurt Christoph Graf von Schwerin, Prussian field marshal (died 1757)
- December 3 – Ludvig Holberg, Norwegian historian and writer (died 1754)
- April 1 – Roger Williams, English theologian and colonist (born 1603)
- April 5 – Lord William Brouncker, English mathematician (born 1602)
- May 4 – John Nevison, English highwayman (born 1639)
- May 12 – Edme Mariotte, French physicist and priest (born c.1620)
- July 2 – John Rogers, American President of Harvard University (born 1630)
- July 6 – Peter Gunning, English royalist churchman (born 1614)
- August 8 – George Booth, 1st Baron Delamer (born 1622)
- October 1 – Pierre Corneille, French playwright (born 1606)
- October 11 – James Tuchet, 3rd Earl of Castlehaven (born 1617)