1684 (MDCLXXXIV) was a leap year starting on Saturday of the Gregorian calendar and a leap year starting on Tuesday of the Julian calendar, the 1684th year of the Common Era (CE) and Anno Domini (AD) designations, the 684th year of the 2nd millennium, the 84th year of the 17th century, and the 5th year of the 1680s decade. As of the start of 1684, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.
King Charles II of England gives the title Duke of St Albans to Charles Beauclerk, his illegitimate son by Nell Gwyn.
The earliest form of what is now the University of Tokyo (formally chartered in 1877), the Tenmongata, is established in Japan.
January 15 (January 5 O.S.) – To demonstrate that the River Thames, frozen solid during the Great Frost that started in December, is safe to walk upon, "a Coach and six horses drove over the Thames for a wager" and within three days "whole streets of Booths are built on the Thames and thousands of people are continually walking thereon." Sir Richard Newdigate, 2nd Baronet, records the events in his diary.
January 26 – Marcantonio Giustinian is elected Doge of Venice.
January – Edmond Halley, Christopher Wren and Robert Hooke have a conversation in which Hooke later claimed not only to have derived the inverse-square law, but also all the laws of planetary motion attributed to Sir Isaac Newton. Hooke's claim is that in a letter to Newton on 6 January 1680, he first stated the inverse-square law.
February 7 – Morocco retakes control of the city of Tangier from England, which had controlled the North African port since 1661. During the five months prior to evacuation of the English from the city, the Governor, Lord Dartmouth had ordered the destruction of the wall around the city, its fortifications and port facilities that had been built by the English during the occupation.
February 8 – Prince Dumitrașcu Cantacuzino returns to the throne of the principality of Moldavia for a third reign but is overthrown 14 months later on June 25. In 1859, Moldavia will unite with neighboring Wallachia to form the Kingdom of Romania.
February 15 (February 5 O.S.) – The Great Frost in Britain, during which the River Thames was frozen in London and the sea as far as 2 miles (3.2 km) out from land and which started the previous December, ends as the Thames begins to thaw. William Maitland later writes that the Frost, which started in December 1683, "congealed the river Thames to that degree that another city, as it were, was erected thereon; where by the great number of streets and shops, with their rich furniture, it represented a great fair, with a variety of carriages, and diversions of all sorts." During the freeze, there had been great loss of beast and of wildlife, especially birds, and similar reports from across Northern Europe. The Chipperfield's Circus dynasty began during the freeze, with James Chipperfield introducing performing animals to the country at the Frost Fair on the Thames in London.
February 24 – A treaty is signed between European German colonists in Brandenburg-Prussia, and the African chiefs in what is now Ghana to permit the German colonists to build a second fort on the Brandenburger Gold Coast, and the fortress of Dorotheenschanze is built. The area is now the Ghanaian city of Akwida.
March 5 – Pope Innocent XI forms a Holy League with the Habsburg Empire, Venice and Poland, to end Ottoman Turkish rule in Europe.
March 19 – In Japan, the Tenna era ends on the 21st day of the 2nd month of the Chinese calendar of the 4th year of the Tenna era and the Jōkyō era begins as Japan's royal astronomer, Shibukawa Shunkai institutes the Jōkyō calendar to replace Chinese calendar which had been used in Japan since 859 AD, after calculating that the length of the solar year is 365.2417 days.
April 25 – The Morean War begins as the Republic of Venice declares war on the Ottoman Empire for control of the Peloponnese area of Greece, a peninsula which includes Corinth and Sparta and has been referred to by the Ottomans as Morea.
May 18 – The French Navy begins a 10-day bombardment of the Italian city of Genoa in the course of the War of the Reunions between France and the Republic of Genoa. During the fight, the French fleet, commanded by Abraham Duquesne, fires almost 13,000 cannonballs, pausing only during a cease-fire on May 21 and May 22, and uses the new technology of explosive bombs. When the bombardment ends on May 28, two-thirds of the city has been destroyed or damaged.
June 7 – After a siege of six weeks that began on April 27, Luxembourg City is taken by the French Army from control by Spain, and the Grand Duchy of Luxembourg, previously part of the Spanish Netherlands (now Belgium) is acquired by France.
June 27 – Francisco de Távora, the Viceroy of Portuguese India, a small colony located in southwestern India at Goa, issues an order prohibiting indigenous residents from speaking their native language, Konkani, and directs them to learn Portuguese within the next three years.
July 21–August 6 – Morean War: Siege of Santa Maura – The Republic of Venice captures the Ottoman island fortress of Santa Maura.
July 24 – René-Robert Cavelier, Sieur de La Salle sails again from France, with a large expedition designed to establish a French colony on the Gulf of Mexico, at the mouth of the Mississippi River.