House of Fingolfin
During the early years of the First Age, the House of Fingolfin held the lands to the northwest of Beleriand; Hithlum, Nevrast and Gondolin. Of these, the city of Gondolin held until F.A. 510, but Hithlum was overrun by Morgoth in the Nirnaeth Arnoediad, where Fingon was slain (Fingolfin had already met his end in the Dagor Bragollach). The remnant of the House, including Fingon's son Ereinion Gil-galad, were succoured by Círdan in the Grey Havens.[note 1]
After the Nirnaeth, Tuor son of Huor was sent as a messenger to Turgon in Gondolin, and there wedded Turgon's daughter Idril. Thus was the blood of Men introduced into the House, and the descendants of their line were named half-elven, given the choice of whether they were to considered Men or Elves. All these descendants chose to be considered among the Firstborn, except Elrond's brother Elros (who became the first King of Númenor and was a direct ancestor of Aragorn Elessar), and Elrond's daughter Arwen (Queen to Aragorn at the end of the Third Age).
After the Fall of Gondolin, the survivors of the House lived as exiles at the Mouths of Sirion or in the Falas, until Eärendil, descendant of Fingolfin's second son Turgon, sailed into the West to seek the aid of the Valar, who overthrew Morgoth in the War of Wrath in c. F.A. 583.
The House of Fingolfin was probably no more as an entity; the only known descendants were the two Half-elven sons of Eärendil; Elrond and Elros, the patriarch of the Mannish House of Elros and the Kings of Númenor.
Other versions of the legendarium
The last High King of the Noldor, Ereinion Gil-galad, remained in Middle-earth. Despite having been listed as the son of Fingon in the official Silmarillion, Christopher Tolkien later admitted this was an editorial error on his part. Gil-Galad's correct parentage is Orodreth of the House of Finarfin.