The island's first known sighting by Europeans was on 21 August 1821 by the British ship Eliza Francis ( or Eliza Frances ) owned by Edward, Thomas and William Jarvis and commanded by Captain Brown.

Only slightly more than a year later, the first landing on the Antarctic mainland was arguably by the American Captain John Davis, a sealer, who claimed to have set foot there on 7 February 1821, though this is not accepted by all historians.

In 1821, Braille learned of a communication system devised by Captain Charles Barbier of the French Army.

In 1821, Marcos Xiorro a slave owned by Vicente Andino, a Militia Captain who owned a sugar plantation in Bayamón, planned and conspired to lead a slave revolt against the sugar plantation owners and the Spanish Colonial government in Puerto Rico.

* Joseph Bloomfield ( 1753 – 1823 ), Captain in Revolutionary War, New Jersey Attorney General, Chief Justice of the New Jersey Vice-Admiralty Court, president of the first Society for the Abolition of Slavery, Mayor from 1795 to 1800, Governor of New Jersey ( 1801 – 1802 and 1803 – 1812 ), a Brigadier General in the War of 1812 and U. S. Representative from 1817 to 1821.

After a meager education, he was apprenticed in 1821 at age 17, to Captain Benjamin Lawrence, a prosperous Middlebury blacksmith, and entered the trade for himself in 1825.

In 1821 Captain Robertson retired to Beverley, where the boy was educated.

Earlier, Guatemala had been a state within the United Provinces of Central America since 1823, before that part of the First Mexican Empire under Agustín de Iturbide, and before 1821 ruled by the Captain General of Guatemala, a Spanish colonial official owing allegiance to the Viceroy of New Spain and the King of Spain, back to the Spanish conquest of the region in the early 16th century.

Known as Lord John Bentinck, he served in the army from 1818, entering it as an Ensign in the Foot Guards and later transferred to the 7th Light Dragoon Guards in 1821, where he became a Captain, the 2nd Life Guards in 1823.

On December 11, 1821, officials from the United States arrived aboard the vessel Alligator under the command of Captain Robert F. Stockton at Mesurado Bay.

Four successive expeditions whose routes took in the Canberra area were those of Charles Throsby Smith ( 1820 ), Charles Throsby ( 1821 ), Major John Ovens and Captain Mark Currie ( 1823 ), and Allan Cunningham ( 1824 ).

The region was explored in 1821 by Captain Roland, who was searching for farm land.

Gray, Kirby prepared the natural history supplement for Captain Parry's 1819 – 1820 expedition to seek the North-West Passage: his work formed the insect section of the Account of the Animals seen by the late Northern Expedition while within the Arctic Circle 1821.

In 1821 he took part in the survey of the Mediterranean coast of Africa under the direction of Captain, afterwards Admiral, William Henry Smyth.

Promoted to Captain in 1813, he commanded Congress in 1817 ; served in Washington in 1818 ; and, in 1819, was placed in command of the Norfolk Station where, in 1821, he established a naval school on the schoolship Guerriere.

In 1819 and 1820, Captain Warrington commanded Java, followed by Guerriere in 1820 and 1821.

The Drummond family was intimately linked to the first educational classes and administrators of the Vila de São Sebastião: Tomé would hold the presidency in 1821, and his older brother, José Ferreira Drummond, was the Ordinance Captain, dominating the local political life for various decades.

Compared with the distinguished officer Edward Berry, who was promoted to Captain in 1797, and was not promoted to Rear-Admiral until 1821, seniority should not have brought promotion to Rear-Admiral to Hornblower until the mid 1830s or later.

The first land grant in the area was made to Captain William Dunn in 1821 on land a few kilometres to the north of Old Banks.

Captain John Hunter ( 1731 – 1821 ) was the first European to explore the area.

Her maternal grandfather was a Captain Stamatis who fought together with Kolokotronis against the Turks in 1821, when the modern Greek democracy was created.

The Robertson Islands were discovered and roughly charted by Captain George Powell and Captain Nathaniel Palmer in December 1821.

It was discovered in December 1821, in the course of the joint cruise by Captain Nathaniel Palmer, an American sailor, and Captain George Powell, a British sailor.

* Frederick William Cumberland ( 1821 – 1881 ), engineer and politician

The US natural gas industry started in 1821 at Fredonia, Chautauqua County, New York, when William Hart dug a well to a depth of into gas-bearing shale, then drilled a borehole further, and piped the natural gas to a nearby inn where it was burned for illumination.

* 1821 – William Poole, American gangster ( d. 1855 )

* 1821 – William Henry Vanderbilt, American businessman ( d. 1885 )

* 1821 – Princess Elizabeth of Clarence, daughter of King William IV, granddaughter of King George III ( b. 1820 )

* 1821 – William Jervois, English engineer and caption, 10th Governor of South Australia ( d. 1897 )

* William I, Elector of Hesse ( 1743 – 1821 )

William Gladstone was educated from 1816 to 1821 at a preparatory school at the vicarage of St Thomas's Church at Seaforth, close to his family's residence, Seaforth House.

In 1821 William followed in the footsteps of his older brothers and attended Eton College before matriculating in 1828 at Christ Church, Oxford, where he read Classics and Mathematics, although he had no great interest in mathematics.

* December 8 – William Henry Vanderbilt, American entrepreneur ( b. 1821 )

* December 11 – William Milligan, Scottish theologian ( b. 1821 )

* March 8 – William Poole, infamous member of New York City's Bowery Boys gang ( b. 1821 )

In 1821 William Conybeare and Henry De la Beche, both members of the Geological Society of London, collaborated on a paper that analysed in detail the specimens found by Anning and others.

William Conybeare named it Plesiosaurus ( near lizard ) because he thought it more like modern reptiles than the ichthyosaur had been, and he described it in the same 1821 paper he co-authored with Henry De la Beche on ichthyosaur anatomy.

This period included a panoply of international ‘ great demographers ’ like Adolphe Quételet ( 1796 – 1874 ), William Farr ( 1807 – 1883 ), Louis-Adolphe Bertillon ( 1821 – 1883 ) and his son Jacques ( 1851 – 1922 ), Joseph Körösi ( 1844 – 1906 ), Anders Nicolas Kaier ( 1838 – 1919 ), Richard Böckh ( 1824 – 1907 ), Émile Durkheim ( 1858-1917 ), Wilhelm Lexis ( 1837 – 1914 ) and Luigi Bodio ( 1840 – 1920 ) contributed to the development of demography and to the toolkit of methods and techniques of demographic analysis.

The first white settler in the area that would become Montgomery County was William Offield, earlier of Tennessee, who arrived in 1821 with his wife Jennie ( née Laughlin ) and one child and settled near the confluence of Offield Creek and Sugar Creek, about five miles ( 8 km ) southwest of Crawfordsville.

* William Irving ( New York ), ( 1766 – 1821 ), U. S. Congressman from New York

* William Thomas Mercer ( 1821 – 1879 ), British Colonial Secretary in Hong Kong, 1859 – 1868

For about 40 years William Kelly ( 1821 – 1906 ) was his chief interpreter and continued to be a staunch supporter until his own death.

During 1821 the President of the Board of Trade, William Huskisson, composed a Commons Committee report which recommended a return to the " practically free " trade of the pre-1815 years.

Its most notable member was the classicist William Kelly ( 1821 – 1906 ).

* William Smith ( congressman ), member of the U. S. House of Representatives from Virginia ( 1821 – 1827 )

* William Durkee Williamson ( 1779 – 1846 ) a governor of Maine ( 1821 ) was born in town.

In 1821, William and Jennie Offield had built a cabin on a little creek, later to be known as Offield Creek, four miles southwest of the future site of Crawfordsville.