Icelandair is the flag carrier of Iceland. It is part of the Icelandair Group and operates to destinations on both sides of the Atlantic Ocean from its main hub at Keflavík International Airport. Its smaller domestic-only hub is located at Reykjavík Airport.

The geographical position of Iceland is convenient for one-stop transatlantic flights via the Atlantic Bridge route, which is one pillar of the airline's business strategy, along with traffic to, from, and within the country. Their headquarters are located in Hafnarfjörður.

Icelandair traces its roots back to 1937, when Flugfélag Akureyrar was founded in Akureyri on the north coast of Iceland. Flight operations started in 1938 with a single Waco YKS-7 configured as a floatplane. In 1939 the airline was grounded when this aircraft was destroyed in a capsizing accident. In March 1940, Flugfélag Akureyrar moved its hub to Reykjavík and moved its operations to fixed-wing seaplane scheduled flights from the Vatnsmýri area, and changed its name to Flugfélag Íslands, where it acquired another Waco aircraft and was relaunched in 1940 as Flugfélag Íslands, which translates as Flight Company of Iceland. Seaplane flights were operated in the vicinity of Vatnsmýri in Skerjafjörður and Vatnagarðar. Previously, the two unrelated airlines of the same name (Flugfélag Íslands) had existed in the country (from 1919 to 1920, and between 1928 and 1931). For international purposes, the name Iceland Airways was adopted.

In 1940, Iceland was invaded by the British and Reykjavík Airport was established south of the capital during the war. In 1946, the airport was handed over to Icelandic civilian authorities, now called Isavia. Iceland Airways (Icelandair) inherited a small building constructed by the British Army on the west side of the airport. Since 1947, the building has been gradually expanded but is still in use by Icelandair as a domestic terminal in 2024. By the 1950s, Iceland Airways operated flights to Britain and Northern Europe from the airport, as well as domestic flights.

The airline was based from Reykjavík Airport, close to the city centre, and the fleet was expanded with a Beechcraft Model 18 in 1942; and with two De Havilland Dragon Rapides and a Consolidated PBY Catalina in 1944, the latter being the first ever aircraft registered in Iceland to be flown to Iceland by an Icelandic crew from North America. On 11 July 1945, this aircraft operated the first commercial flight over the Atlantic Ocean for the airline, which led from Reykjavík to Largs in Scotland, with four passengers and four crew members on board. Regular flights to Prestwick Airport in Scotland and Copenhagen in Denmark, using Consolidated B-24 Liberator aircraft leased from Scottish Airlines were launched in 1946.

In the same year, the comfort and performance of domestic flights in Iceland was improved with the introduction of the Douglas DC-3. A total of six were purchased, which remained in service with the airline until 1972. Until the late 1960s, Flugfélag concentrated mostly on domestic service, but it also continued operating internationally; in 1948, the Douglas DC-4 was introduced on international routes, and in 1957, two new Vickers 759 Viscounts were acquired, the first turboprop airliners to be operated by an Icelandic airline. In the 1950s, Flugfélag began to use Icelandair branding for flights beyond Iceland.

In 1967, Flugfélag was the first Icelandic airline to join the jet age, when a Boeing 727-100 dubbed Gullfaxi was put into service. The B-727 jet aircraft was operated from Keflavík Airport, as the aircraft was considered too large for the smaller Reykjavík Airport. Most of Flugfélag's international operations transferred to Keflavík by this time. This left only shorter-distance flights to Greenland and the Faroes as the only international services from Reykjavík Airport. Another 727 was acquired in 1971, and the aircraft type was operated until 1990. In 2008, the cockpit section of Gullfaxi was put on display at the Akureyri Aviation Museum.

Another company, Loftleiðir, called Icelandic Airlines internationally, was formed in 1944 by three young pilots returning from their flight training in Canada. The company, whose name roughly means "Skyways", initially concentrated on Icelandic domestic routes using two Stinson Reliants and then a Grumman G-21 Goose amphibious aircraft.