[5] In the 2004–05 UEFA Cup, FH defeated Haverfordwest County of Wales in the first qualifying round, and then Scottish side Dunfermline Athletic in the second 4–3 on aggregate.

In summer 2006 three of the club's players played for the national team: Daði Lárusson, Sigurvin Ólafsson and Ármann Smári Björnsson.

Ármann Smári also joined Norwegian team Brann after a superb spell for the first 15 rounds[clarification needed].

Baldur Bett also left the squad at the end of the season and joined rivals Valur on a free transfer.

The club stadium Kaplakriki underwent a major redevelopment: the southern stand expanded, bringing the seating capacity to 3,500.

On 20 October 2006 the club signed the Icelandic twins Arnar and Bjarki Gunnlaugsson, who have played for Bolton Wanderers F.C., Stoke City F.C., Feyenoord Rotterdam, 1.

In one of the most exciting last days of the competition ever, their main rivals Keflavík were odds-on favorites to win the title with a 2-point lead over FH going into the last round.

FH had a game against Fylkir while Keflavík played hosts to Fram, who themselves had to win to secure third place and the last spot in the UEFA Cup next season.

As of July 29, 2021 Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply.