Argja Bóltfelag, often known more simply as AB, was first established in August 1973 and began regular competitive play the following year. Throughout history, the club have spent most of their time in the lower divisions of the Faroe Islands' league pyramid, but have grown in stature since the turn of the millennium. Their nickname is 'Frensurin'.
Based in the village of Argir, the team originally had to play home matches in Tórshavn, due to the absence of a football field in their home village. During this time, they also had to utilise a school playground for training purposes. This changed in the early 1980s, when a football field was installed and gradually the club's facilities have improved ever since.
Tórálvur Stenberg took over as the club's chairman in 2000 and masterminded their dramatic rise to prominence. During his time in the role, the club was able to gain promotion from the country's third tier all the way up to the Faroe Islands Premier League, which they eventually reached in 2006. Unfortunately, Stenberg passed away before he was able to see the team make their debut in the division. Their first season was largely unsuccessful and resulted in relegation, but AB were able to return to the top flight after just one season back in the second tier.
Notable players to represent the club have included Rúni Nolsøe, Allan Mørkøre and Rógvi Poulsen. In addition, two of Tórálvur Stenberg's sons, Jónas and Heðin Stenberg, currently play for the side, continuing his legacy. Jónas Stenberg was named the club's player of the year for the 2007 season.
AB's home matches are now played at Argir Stadium, which is also sometimes known as Inni í Vika Stadium. It underwent renovations in 2010 and is currently able to hold up to 2,000 supporters.