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Breiðablik's first competitive match was played on 12 June 1957, a 1–0 loss against Þróttur Reykjavík. After several years in the lower leagues, Breiðablik competed in the country's top division, the Úrvalsdeild karla (Úrvalsdeild), for the first time in 1971. From 1971 to 2005, Breiðablik would bounce between the two top leagues in Iceland (Úrvalsdeild and second-tier 1. deild karla), being promoted and relegated on a regular basis.

Since being promoted into the 2006 Úrvalsdeild, Breiðablik men's team has established itself as a powerhouse in Iceland, challenging regularly on all fronts. As of completion of the COVID-19 shortened 2020 Úrvalsdeild, Breiðablik has earned a place in their 17th consecutive season in the Úrvalsdeild.

The team's first major trophy came with a win in the 2009 Icelandic Cup, followed by the team's first Úrvalsdeild champions title in 2010. Their 2009 Icelandic Cup win qualified them for their first ever European competition, entering the second qualifying round of the 2010–11 UEFA Europa League, facing Scottish Premier League side Motherwell. They lost the first leg 1–0 in Scotland, and lost by the same score in the return leg, for a loss of 0–2 on aggregate. Their 2010 Úrvalsdeild title took Breiðablik to their second consecutive European competition, entering the second qualifying round of the 2011–12 UEFA Champions League, facing Norwegian Tippeligaen champion Rosenborg, losing 2–5 on aggregate. Breiðablik won its first match in a European competition in the first qualifying round of the 2013–14 UEFA Europa League, with a 4–0 win in the first leg against Andorran Copa Constitució winner FC Santa Coloma, en route to their first aggregate win (4–0) of a round in a European competition.

With one of the largest youth facilities in Iceland, Breiðablik is almost entirely built on home-grown talent. In the early 2000s, Iceland national football team internationals who came through the Breiðablik youth ranks included: Jóhann Berg Guðmundsson (first senior national team cap in 2008); Guðmundur Kristjánsson (2009); Alfreð Finnbogason and Gylfi Sigurðsson (both in 2010).