1737

January–March

• January 5 - Spain and the Holy Roman Empire sign instruments of cession at Pontremoli in the Grand Duchy of Tuscany in Italy, with the Empire receiving control of Tuscany and the Grand Duchy of Parma and Piacenza, in return for Don Carlos of Spain being recognized as King of Naples and King of Sicily.
• January 9 - The Empires of Austria and Russia enter into a secret military alliance that leads to Austria's disastrous entry into the Russo-Turkish War.
• January 18 - In Manila, a peace treaty is signed between Spain's Governor-General of the Philippines, Fernándo Valdés y Tamon, and the Sultan Azim ud-Din I of Sulu, recognizing Azim's authority over the islands of the Sulu Archipelago.
• February 16 - George Frideric Handel's opera Giustino is performed for the first time, premiering in London at the Theatre Royal.
• February 20 - France's Foreign Minister, Germain Louis Chauvelin, is fired by King Louis XV's Chief Minister, Cardinal André-Hercule de Fleury
• February 27 - French scientists Henri-Louis Duhamel du Monceau and Georges-Louis Leclerc de Buffon publish the first study of correlating past weather conditions with an examination of tree rings), "On the cause of the eccentricity of the woody layers which one perceives when one cuts horizontally the trunk of a tree"
• March 16 - In Paris, representatives of Spain and Portugal sign an armistice bringing and end to the Spanish–Portuguese War over the area now occupied by the nation of Uruguay and the area now occupied by the state of Rio Grande do Sul in Brazil. The news does not reach the fighting parties until five months later.
• March 28 - The Battle of Delhi takes place between the Maratha Empire and the Mughals.

  April–June

• April 5 -French Jesuit priest Jean-François Régis is canonized as Saint Regis by the Roman Catholic Church under the reign of Pope Clement XII.
• April 22 -
• *In Afghanistan, Persian shah Nader Shah begins the 11-month Siege of Kandahar against the Pashtun Emir of Afghanistan, Hussain Hotak. The surviving Afghanis surrender on March 24. p613
• *Lots are first advertised for sale in the new town of Richmond, Virginia, by the placement of a notice by William Byrd in the Virginia Gazette. According to the paper, "... on the North Side of James River, near the Uppermost Landing, and a little below the Falls, is lately laid off by Major Mayo, a Town, called Richmond, with Streets 65 Feet wide, in a pleasant and healthy Situation, and well supply'd with Springs of good Water. It lies near the Publick Warehouse at Shoccoe's, and in the midst of great Quantities of Grain, and all kind of Provisions. The Lots will be granted in Fee Simple, on Condition only of building a House in Three Years Time, of 24 by 16 Feet, fronting within 5 Feet of the Street. The Lots to be rated according to the Convenience of their Situation, and to be sold after this April General Court, by me, William Byrd."
• May 28 - The planet Venus passes in front of Mercury. The event is witnessed during the evening hours, by the amateur astronomer John Bevis, at the Royal Greenwich Observatory. As of 2006, it is still the only such planet/planet occultation that has been directly observed.
• June 21 - In Britain, the Theatrical Licensing Act requires plays to be submitted to the Lord Chamberlain for censorship.
• June 30 - Russo-Turkish War, 1735-1739: Russian forces under Field Marshal Munnich storm the Ottoman fortress of Ochakov, and take prisoner 4,000 Turks.

  July–September

• July 12 - Austria enters the Russo-Turkish War as an ally of Russia against the Ottoman Empire.
• July 17 - The British ship Catherine founders in a storm off of Nova Scotia's Cape Sable Island during its voyage from Ireland to Boston, killing 98 of the 201 people on board.
• August 4 - Austria's army is defeated by the Ottoman Army and Bosnian defenders in the Battle of Banja Luka.
• August 15 - The Portuguese frigate Nossa Senhora da Boa Viagem arrives at Maldonado as Captain Duarte Pereira brings the news that the Spanish–Portuguese War ended by an agreement signed on March 16.
• September 1 - The oldest existing English language newspaper in the world, The News Letter, is founded in Belfast, Ireland.
• September 20 - Runner Edward Marshall completes his journey in the Walking Purchase, forcing the cession of of Lenape-Delaware tribal land to the Pennsylvania Colony.

  October–December

• October 7 - At least 300,000 people are killed when a tropical cyclone strikes the Bay of Bengal in India and modern-day Bangladesh. The storm sends high waves over the Sundarbans delta, and overflows the Hooghly River.
• October 11 - The first national stage in Sweden opens, when Carl Gyllenborg's play Den svenska sprätthöken is performed in the Swedish language, by the first native actors, on the stage of Bollhuset in Stockholm.
• October 16 - An earthquake with an estimated magnitude of 9.3 occurs off the shore of Russia's Kamchatka Peninsula. Tsunamis up to high follow in the Pacific ocean.
• November 4 - The Teatro di San Carlo, the oldest working opera house in Europe, is inaugurated in Naples, Italy.
• December 24 - General Baji Rao of the Maratha Empire in India defeats the armies of the rulers of Hyderabad, Oudh, Bhopal and Jaipur in the Battle of Bhopal.

  Date unknown

• Benjamin Franklin creates the Philadelphia Police Force - the first city-paid force in 1737.
• The Georg August University of Göttingen is founded.
• The direct male line of the Medici family becomes extinct, with the death of Gian Gastone de' Medici, Grand Duke of Tuscany.
• Richmond, Virginia is founded.
• Our Lady of Guadalupe is designated the patron saint of Mexico City.
• Lancaster County Prison, Lancaster, Pennsylvania is first constructed, in response to the seven preceding violent years of the ongoing Cresap's War, in the Maryland-Pennsylvania boundary dispute and war.