- May 5 - Indian Wars: Sitting Bull leads his band of Lakota into Canada to avoid harassment by the United States Army under Colonel Nelson Miles.
- May 6 - Realizing that his people were weakened by cold and hunger, Chief Crazy Horse of the Oglala Sioux surrenders to United States troops in Nebraska.
- May 8 - At Gilmore's Gardens in New York City, the first Westminster Kennel Club Dog Show opens (ends May 11).
- May 10 - Romania declares itself independent from Turkey (recognized in 1881 after the end of the Romanian independence war).
- May 16 - Romania declares war on Turkey
- June 15 - Henry Ossian Flipper becomes the first African American cadet to graduate from the United States Military Academy.
- June 21 - The Molly Maquires hanged at Carbon County prison in Jim Thorpe, Pennsylvania
- June 26 - Eruption of Mount Cotopaxi in Ecuador causes severe mudflows that wipe out surrounding cities and valleys - 1000 dead
- June 30 - British Mediterranean fleet is sent to Besika Bay
- July 9 - All England Croquet and Lawn Tennis Club begins its first lawn tennis tournament at Wimbledon.
- July 19 - First battle in the Siege of Pleven.
- July 21 - A day after bloody rioting in Baltimore from Baltimore and Ohio Railroad workers and the deaths of 9 rail workers at the hands of the Maryland militia, workers in Pittsburgh stage a sympathy strike that is met with an assault by the state militia - Pittsburgh then erupts into widespread rioting.
- July 30 - Second battle in the Siege of Pleven.
- August 9 - Indian Wars: Battle of Big Hole - Near Big Hole River in Montana, a small band of Nez Percé Indians who refused government orders to move to a reservation, clash with the United States Army. The army lost 29 soldiers and Indians lost 89 warriors in a US Army win.
- August 12 - Asaph Hall discovers Deimos, outer moon of Mars.
- August 17 - Arizona blacksmith F.P. Cahill is fatally wounded by Billy the Kid. Cahill will die the next day, becoming the first person killed by the Kid.
- August 18 - Asaph Hall discovers Phobos, inner moon of Mars.
September - December
- September 1 - Battle of Lovcha, Third battle in the Siege of Pleven.
- September 5 - Indian Wars: Oglala Sioux chief Crazy Horse is bayoneted by a United States soldier after resisting confinement in a guardhouse at Fort Robinson in Nebraska.
- October 10 - Following the recovery of Lieutenant-Colonel George Armstrong Custer's body from where he fell during the Battle of Little Big Horn the previous year, Custer is given a funeral with full military honors and is laid to rest at the United States Military Academy at West Point, New York.
- November 21 - Thomas Edison announces his invention of the phonograph, a machine that can record sound (this is considered to be Edison's first great invention) (Edison demonstrated the device for the first time on November 29).
- December 9 - Fourth battle, concluding the Siege of Pleven.
- December 14 - Serbia restates its previous declaration of war against Turkey
- War between Russia and the Ottoman Empire (Russo-Turkish War), leading to the formation of Bulgaria in 1878. See Russian Foreign Affairs after the Crimean War.
- Nineteenth Century magazine founded.
- January 2 - Slava Raskaj, Croatian painter (d. 1906)
- February 7 - G. H. Hardy, British mathematician (d. 1947)
- February 14 - Edmund Landau, German mathematician (d. 1938)
- February 17 - André Maginot, French politician (d. 1932)
- February 19 - Gabriele Münter, German painter (d. 1962)
- February 25 - Erich von Hornbostel, Austrain musicologist (d. 1935)
- March 2 - Consuelo Vanderbilt, Duchess of Marlborough (d. 1964)
- March 16 - Reza Pahlavi, Shah of Iran (d. 1944)
- March 18 - Edgar Cayce, American psychic (d. 1945)
- May 3 - Karl Abraham, German psychoanalyst (d. 1925)
- June 4 - Heinrich Otto Wieland, German chemist, Nobel Prize laureate (d. 1957)
- June 7 - Charles Glover Barkla, English phyicist, Nobel Prize laureate (d. 1944)
- June 14 - Jane Bathori, French opera singer (d. 1970)
- July 2 - Hermann Hesse, German-born writer, Nobel Prize laureate (d. 1962)
- July 6 - Arnaud Massy, French golfer (d. 1950)
- July 13 - Erik Scavenius, Prime Minister of Denmark (d. 1962)
- July 19 - Arthur Fielder, English cricketer (d. 1949)
- July 17 - Ernst von Dohnanyi, Hungarian conductor (d. 1960)
- August 6 - Wallace H. White, Jr., U.S. Senator from Maine (d. 1952)
- August 7 - Ulrich Salchow, Swedish figure skater (d. 1949)
- September 1 - Francis William Aston, English chemist, Nobel Prize laureate (d. 1945)
- September 2 - Frederick Soddy, English chemist, Nobel Prize laureate (d. 1956)
- September 6 - Buddy Bolden, American jazz musician (d. 1930)
- September 26 - Alfred Cortot, Swiss pianist (d. 1962)
- October 4 - Razor Smith, English cricketer (d. 1946)
- October 27 - George Thompson, English cricketer (d. 1943)
- November 9 - Allama Iqbal, Indian philosopher and poet (d. 1938)
- November 22 - Endre Ady, Hungarian poet (d. 1919)
- December 3 - Richard Pearse, New Zealand airplane pioneer (d. 1953)
- Alois Kayser, German missionary (d. 1944)
- January 4 - Cornelius Vanderbilt, American entrepreneur (b. 1794)
- August 29 - Brigham Young, American Mormon leader (b. 1801)
- September 2 - Constantine Kanaris, Greek politician (b. 1795)
- September 5 - Crazy Horse, Oglala Sioux chidf (b. 1849)
- October 16 - Theodore Barrière, French dramatist (b. 1823)
- November 2 - Friedrich Graf von Wrangel, Prussian field marshal (b. 1784)
- December 31 - Gustave Courbet, French painter (b. 1819)
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