The American Revolution begins this year, with the first military engagement being the April 19 Battles of Lexington and Concord on the day after Paul Revere's now-epic ride. The Second Continental Congress takes various steps toward organizing an American government, appointing George Washington commander-in-chief (June 14), Benjamin Franklin postmaster general (July 26) and creating a Continental Navy (October 13) and a Marine force (November 10) as landing troops for it, but as yet the 13 colonies have not declared independence, and both the British (June 12) and American (July 15) governments make laws. On July 6, Congress issues the Declaration of the Causes and Necessity of Taking Up Arms, and on August 23, King George III of England declares the American colonies in rebellion, announcing it to Parliament on November 10. On June 17, two months into the colonial siege of Boston, at the Battle of Bunker Hill, just north of Boston, British forces are victorious, but only after suffering severe casualties and after Colonial forces run out of ammunition, Fort Ticonderoga is taken by American forces in New York Colony's northern frontier, and American forces unsuccessfully invade Canada, with an attack on Montreal defeated by British forces on November 13 and an attack on Quebec repulsed December 31.
Human knowledge and technology advances when James Watt builds a successful prototype of a steam engine, and a scientific expedition continues as Captain James Cook claims the South Georgia and South Sandwich Islands in the south Atlantic Ocean for Britain. Nature's power over humanity is dramatically demonstrated when the Independence Hurricane (August 29 – September 13) devastates the east coast of North America, killing 4,173, and when a smallpox epidemic begins in New England.
- January – The Habsburg Monarchy forces the Ottoman Empire to cede Bukovina to its rule.
- January 5 – Wolfgang Amadeus Mozart finishes a Sonata for Keyboard in C.
- January 11— Francis Salvador is elected to the Provincial Congress of South Carolina, becoming the first Jewish public officeholder in North America. 
- January 16–20 – Second voyage of James Cook: Captain James Cook circumnavigates, makes the first landing on and (on January 17) takes possession of South Georgia in the southern Atlantic Ocean, for the Kingdom of Great Britain. The following month he discovers the South Sandwich Islands.
- February 9 – American Revolution: The Parliament of Great Britain declares the Province of Massachusetts Bay to be in rebellion.
- February 15 – Pope Pius VI succeeds Pope Clement XIV, as the 250th pope.
- March 6 – Raghunathrao, Peshwa of the Maratha Empire in India, signs the Treaty of Surat with British Governor-General Warren Hastings in Bombay, ceding the territories of Salsette and Bassein to the British East India Company, along with part of the revenues from Surat and Bharuch districts, in return for military assistance. This leads to the First Anglo-Maratha War, fought between the British and the Marathas, ending with the Treaty of Salbai in 1782.
- March 10 — Daniel Boone begins blazing the widely-used Wilderness Road used by white settlers to reach Kentucky and Tennessee. 
- March 17 – Catherine the Great of Russia issues a manifesto, prohibiting freed serfs from being returned to serfdom.
- March 23 – American Revolution: Patrick Henry, a delegate to the Second Virginia Convention after the Virginia House of Burgesses was disbanded by the Royal Governor, delivers his Give me liberty, or give me death! speech at St. John's Church in Richmond, Virginia.
- April 14 – The first anti-slavery society in the United States is formed by a group of Quakers in Philadelphia.  
- April 18 – American Revolution: Paul Revere and William Dawes, instructed by Dr. Joseph Warren, ride from Boston to Lexington, to warn John Hancock and Sam Adams that British forces are coming to take them prisoner, and to seize colonial weapons and ammunition in Concord.
- April 19 – American Revolution – Battles of Lexington and Concord: Hostility between Britain and its American colonies explodes into bloodshed,  igniting the American Revolution.
- May 9 – American Revolution: Brunswick militiamen commanded by Samuel Thompson capture Henry Mowat, captain of HMS Canceaux.
- May 10
- May 14 – American Revolution – Battle off Fairhaven: In the first naval engagement of the American Revolutionary War, Patriots recover two Patriot vessels, and capture 13 Royal Navy sailors as prisoners of war.
- May 17 – American Revolution: The Continental Congress bans trade with Canada.
- May 20
- American Revolution – Battle of Lexington: American militiamen drive British troops back to Boston.
- The Committee of Mecklenburg County, North Carolina ratifies the Mecklenburg Declaration of Independence, dissolving allegiance to the Royal Crown of England, becoming the first collective to declare sovereignty in the Royal Colonies.
- May 24 — John Hancock is selected as the President of the Second Continental Congress. 
- May 29— The Congress adopts its "Address to the Inhabitants of Canada". 
- June 11 – Battle of Machias: In the second naval engagement of the American Revolutionary War, American forces capture the schooner HMS Margaretta.
- June 12 – American Revolution:
- June 14 – American Revolution: The Continental Congress names George Washington as commander of the Continental Army.
- June 16 – The post of Chief Engineer of the Continental Army is created.
- June 17 – American Revolution: Two months into the colonial siege of Boston, British open fire on Breed's Hill on Charles Town Peninsula. After 3 charges, the British take the hill, in the misnamed Battle of Bunker Hill.
- June 19 – American Revolution: The post of Commanding General is created by the Continental Congress.
- June 25 – The Great Fire of Tartu, Governorate of Livonia, destroys most of the town.
- July 3 – American Revolution: George Washington takes command of the 17,000-man Continental Army at Cambridge.
- July 5 – American Revolution: The Continental Congress sends the Olive Branch Petition, hoping for a reconciliation.
- July 6 – American Revolution: The Continental Congress issues the Declaration of the Causes and Necessity of Taking Up Arms, which contains the words: "Our cause is just. Our union is perfect... being with one mind resolved to die freemen rather than to live slaves...".
- July 8 – Congress adopts its second petition to King George III. 
- July 25— Dr. Benjamin Church becomes the first Surgeon General of the Contineal Army. 
- July 26 – The Second Continental Congress appoints Benjamin Franklin to be the first Postmaster General, of what later becomes the United States Post Office Department. Franklin establishes posts from Falmouth, Maine to Savannah, Georgia. 
- July 28 — The Congress adopts its "Address to the People of Ireland". 
- July 29 — Michael Hillegas and George Clymer are hired by the Congress to be the "joint treasurers of the United Colonies." 
- July 30 – Second voyage of James Cook: HMS Resolution anchors off the south coast of England, Captain Cook having completed the first eastabout global circumnavigation.
- August 18 – Tucson is founded.
- August 21 – American Revolution – Siege of Fort St. Jean: American rebels launch an invasion of Canada.
- August 23 – American Revolution: Refusing to even look at the Olive Branch Petition, King George III issues a Proclamation of Rebellion against the American colonies.
- August 29–September 12 – The Independence Hurricane from South Carolina to Nova Scotia kills 4,170, mostly fishermen and sailors.
- September 8 – The unsuccessful Rising of the Priests takes place in Malta.
- September 25 – American Revolution – Siege of Fort St. Jean – Battle of Longue-Pointe: Thirteen Colonies revolutionary forces under Maj. Ethan Allen attack Montreal, Quebec, commanded by British General Guy Carleton. Allen's forces are defeated, and Allen himself is captured and held on British ships, until he is later released.