| 1800–1850 | USA [consumer products] | A revolution in retail and wholesale trade occurs: specialization transforms the urban retail market, replacing the general store with individual stores for hardware, groceries, dry goods, furnishing, books, tobacco, and so on. Cash-only sales policies are instituted around 1806. |
| 1810–1859 | USA [agriculture] | US cotton production, the vast majority of which is grown in the southern states, rises from 171,000 bales in 1810 to just under 5.4 million in 1859. |
| 1840–1850 | USA [farming] | Wheat becomes an increasingly important cash crop in the USA; production in 1839 is nearly 85 million bushels and climbs to over 100 million bushels in 10 years. |
| 1840–1860 | world [plagues and epidemics] | A cholera pandemic kills millions of people worldwide. |
| 1841–1850 | USA, UK [statistics and demography] | Emigration to the USA is 267,044 from Britain and 780,719 from Ireland. |
| 1842–1845 | UK [astronomy] | Irish astronomer William Parsons (later Lord Rosse) builds the 180 cm/72 in reflecting telescope ‘Leviathan’. |
| 1845 | Germany [economic theory] | The German political writer Friedrich Engels publishes Die Lage der arbeitenden Klasse in England/The Condition of the Working Classes in England, a classic of communism. |
| 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. |
| 1845 | Scotland [transport] | Scottish inventor Robert Thomson patents the pneumatic tyre. Although used for 1,930 km/1,200 mi on a horsedrawn brougham carriage, pneumatic tyres are not used again until the end of the century. |
| 1845 | USA [poetry] | The US writer Edgar Allan Poe publishes The Raven and Other Poems. |
| 1845 | UK [consumer products] | Henry Jones of Bristol, England, creates self-raising flour. |
| 1845 | [maths] | English mathematician Arthur Cayley publishes Theory of Linear Transformations. He studies compositions of linear transformations. |
| c. 1845 | USA [painting] | The US artist George Caleb Bingham paints Fur Traders Descending the Missouri. |
| 1845 | Europe [agriculture] | The potato blight fungus Phytophthora infestans causes potato crops to fail throughout Europe. In Ireland, where the potato is a staple, over half the crop is lost causing devastating famine. Over 1 million die and 1.5 million emigrate over the next 2 years. |
| 11 March 1845 | New Zealand, UK [law and government] | Further Maori risings take place against British rule in New Zealand, following revolts in 1843 and 1844. |
| 13 September 1845 | USA [baseball] | The Knickerbocker Club, New York City, codifies the rules of baseball. |
| 23 October 1845 | France [births and deaths] | Sarah Bernhardt, French actor, born in Paris, France (–1923). |
| 11 December 1845 | India, UK [wars] | The First Anglo-Sikh War breaks out in northwest India when the powerful Sikh army crosses the Sutlej River to attack British territories in central Hindustan, after a period of growing tension following the death of the Sikh maharaja Ranjit Singh. |
| 29 December 1845 | Republic of Texas, USA [political events] | Texas becomes a US state. |
