| 1845–1958 | Germany [earth sciences] | German naturalist and explorer Alexander von Humboldt lays the basis of modern geography with the publication of Kosmos/Cosmos, in which he arranges geographic knowledge in a systematic fashion. |
| 1861–1865 | USA [economic conditions] | The USA, or the North, has a booming economy during the Civil War as production and profits soar. There is inflation, too; prices rise 117% and wages rise just 43%. |
| 1861–1870 | USA, UK, Ireland [statistics and demography] | Emigration to the USA from Britain totals 606,896; from Ireland it is 435,779. |
| 1864 | UK [unions and associations] | The (First) International Working Men's Association is founded in London, England, by the German philosopher, economist, and social theorist Karl Marx to coordinate the activities of workers' associations worldwide. |
| 1864 | England [astronomy] | By examining their spectra, English astronomer William Huggins demonstrates that the Orion Nebula (and hence all nebulae) consists of gases, while the Andromeda Nebula is composed of stars and is therefore a galaxy. |
| 1864 | Russia [fiction] | The Russian writer Leo Tolstoy publishes the first part of his epic novel Voyna i mir/War and Peace. The second part appears in 1869. |
| 1864 | Russia [fiction] | The Russian writer Fyodor Mikhaylovich Dostoyevsky publishes his novel Zapiski iz podpolya/Notes from the Underground. |
| 1864 | France [materials] | French engineers Pierre and Emile Martin use scrap iron in place of iron ore in a Siemens regenerative furnace. Two years later Siemens and the Martins combine to produce the Siemens-Martin open-hearth furnace. |
| 1864 | Scotland [physics] | Scottish physicist James Clerk Maxwell introduces mathematical equations that describe the electromagnetic field, and predict the existence of radio waves. |
| 1864 | UK [public health] | As venereal disease becomes rife in the armed forces, the British government passes legislation to monitor the health of prostitutes. |
| 1 February 1864 | Austrian Empire, Prussia, Germany, Denmark [political events] | Austro-Prussian troops enter Schleswig in opposition to Denmark's incorporation of the disputed territory. |
| 10 April 1864 | Austrian Empire, Mexico, France [political events] | Archduke Maximilian of Austria accepts the title offered by Napoleon III of emperor of Mexico, following French military victories there in an attempt to enforce the payment of European debts. France wishes to establish a liberal, Catholic empire in Mexico. |
| 5 May - 6 May 1864 | USA [American Civil War (1861–65)] | The Union under General Ulysses S Grant and the Confederates under General Robert E Lee fight the indecisive Battle of the Wilderness, Virginia. |
| June 1864 | USA, Confederate States of America [American Civil War (1861–65)] | At the Battle of Cold Harbor, Virginia, a Confederate army repels a Union army nearly twice its size. In the aftermath, Union general Grant begins a prolonged siege of Petersburg, Virginia, that will last to the end of the war. |
| 23 August 1864 | Crete [births and deaths] | Eleutherios Venizelos, Greek politician, prime minister of Greece 1910–15, 1917, 1924, and 1928–30, born in Mourniés, Crete (–1936). |
| 30 October 1864 | Austrian Empire, Prussia, Denmark [treaties] | The Peace of Vienna concludes the German-Danish war, by which Denmark cedes the duchies of Schleswig, Holstein, and Lauenburg to Austria and Prussia. |
| 8 November 1864 | USA [elections] | Abraham Lincoln is re-elected as US president, and Andrew Johnson as vice-president. |
| 24 November 1864 | France [births and deaths] | Henri de Toulouse-Lautrec, French artist who depicts the personalities of Parisian night life, born in Albi, France (–1901). |
| 28 November 1864 | Greece [administration] | An advanced new democratic constitution in Greece does away with the upper Chamber of Deputies. |
| 8 December 1864 | Ireland, England [births and deaths] | George Boole, English mathematician who developed Boolean algebra, which is central to computer operations, dies in Ballintemple, Ireland (49). |
| 8 December 1864 | Rome [Catholicism] | A papal Syllabus Errorum/Syllabus of Errors condemns the errors of the 19th century – nationalism, naturalism, socialism, communism, and freemasonry. |
