Bjarni Herjólfsson (fl. 10th century) was a Norse explorer who is the first known European discoverer of the mainland of the Americas, which he sighted in 985 or 986.

Bjarni was born to Herjólfr son of Bárdi Herjólfsson (Old Norse: Bárði), and Thorgerdr (Old Norse: Þorgerðr) in Iceland. In adulthood, Bjarni became a merchant captain, based in Norway, but visiting his father every summer in Iceland.

Bjarni is believed to have been the first European to see North America. The Grœnlendinga saga ('Greenlanders Saga') tells that one year he sailed to Iceland to visit his parents as usual, only to find that his father had gone with Eric the Red to Greenland. So he took his crew and set off to find him. But in that summer of 985 or 986, Bjarni was blown off course by a storm with no map or compass. He saw a piece of land that was not Greenland. It was covered with trees and mountains and although his crew begged him to, he refused to stop and look around. Since no one in his crew had been to Greenland before, they had to search for it. Although he managed to regain his course, he reported seeing low-lying hills covered with forests some distance farther to the west. The land looked hospitable, but Bjarni was eager to reach Greenland to see his parents and did not land and explore the new lands. Eventually arriving in Greenland, he decided to settle with his father. He reported his findings in Greenland but no one seems to have shown interest in them until, after his father's death, he returned to Norway.

Bjarni Harðarson (born in Hveragerði on December 25, 1961) is a bookseller and former MP from the Icelandic Progressive Party. He was elected to parliament in 2007 as the eighth MP from the Suðurkjördæmi electoral district.

On November 10, 2008, he was involved in a political scandal; when a document of his that contained strong criticism of Valgerður Sverrisdóttir, vice chairman of the Progressive Party, was mistakenly leaked. The day after, Bjarni resigned from parliament.

In the 2009 election, Bjarni ran as a candidate for the L-List of Sovereignty Supporters. He did not win a seat in the Althing.

Bjarni Benediktsson (30 April 1908 – 10 July 1970) was Prime Minister of Iceland from 14 November 1963 to 10 July 1970. His father, Benedikt Sveinsson (1877–1954), was a leader in the independence movement in Iceland and a member of Althingi from 1908 to 1931.

Bjarni studied constitutional law and became professor at the University of Iceland at the age of only 24. He was elected to the city council in Reykjavík in 1934 as a member of the Independence Party and from 1940 to 1947 was mayor of the city.

In 1947 he became Foreign Minister and served in various posts in cabinets until 1956. His tenure included the establishment of Iceland as a founding member of NATO in 1949. In 1956, when the left-wing parties formed a coalition government, Bjarni, out of office, became editor of Morgunblaðið, a leading conservative newspaper.

In 1959, when the Independence Party formed a coalition government with the Social Democrats, Bjarni became Minister of Justice. Two years later he was elected chairman of the Independence Party and in 1963 he took over from Ólafur Thors as Prime Minister. He served in this position until his death, which was caused by a fire at a government summer house at Þingvellir; his wife and grandson also perished in the blaze.

Bjarni Jónsson (born 1920) is an Icelandic mathematician and logician working in universal algebra and lattice theory. He is emeritus Distinguished Professor of Mathematics at Vanderbilt University and the honorary editor in chief of Algebra Universalis. He received his PhD in 1946 at UC Berkeley under supervision of Alfred Tarski.

Several mathematical objects are named for him, among them Jónsson algebras, ω-Jónsson functions, Jónsson cardinals, Jónsson terms, and Jónsson–Tarski duality.

Jónsson is the father of author and communications trainer Meryl Runion, whose Speak Strong Speak Strong Web site training methods have been used by the US Army, FBI, IBM, and Fortune 500 companies to train staff how to communicate effectively.