Iceland was a nation in western Europe.
According to Jack Harkness, the Icelandic race were of alien origin, possibly from the vicinity of Pyrovillia. They crashed on Earth while investigating the volcanoes of Iceland. (AUDIO: The Sin Eaters)
In 1984, Major Whitaker of UNIT and Dr Iskander explored an Icelandic volcano to investigate an unnatural increase in volcanic and seismic activity; they found the source to be the Dominator Haag and his Quarks, who had set up base there. (COMIC: The Fires Down Below)
Near the year 2010, Icelandic banks became unsound, leaving depositors and investors in financial difficulties. Lady Christina de Souza told the Tenth Doctor that the reason she became a thief was that her father had lost his money in this financial debacle. (TV: Planet of the Dead)
In the 51st century, Iceland was part of the Icelandic Alliance. It lost a war to the Supreme Alliance of Eastern States and was occupied until the Filipino Army liberated Reykjavik in the Battle of Reykjavik. (TV: The Talons of Weng-Chiang, AUDIO: The Butcher of Brisbane)