B36 in their new away colours against TB Tvøroyri on 15 April 2012. The player is Símun Hansen.
B36 Tórshavn was founded on 28 March 1936. B36 started to play football matches in 1935, but were officially founded in 1936. B36 has an arch rival, HB Tórshavn, which was founded in 1904, the first club in Tórshavn.
But the rivalry has a limit, when B36 Tórshavn were going to publish an official book in 1997, they used HB Tórshavn's book as the main source. B36 Tórshavn's first documents got lost, that's why HB Tórshavn's book had to be used. When B36 was founded, they battled with rivals HB Tórshavn for the rights to the Gundadalur Stadium, but the teams played a lot of matches against each other that year.
B36 Tórshavn had a hard time by getting accepted by the main newspaper in the Faroe Islands, but after half a year B36 Tórshavn had achieved some good results, that resulted in that journalists had no other option but to accept B36 Tórshavn. Today, B36 Tórshavn is one of the biggest football clubs in the Faroe Islands.
Clubs in the Faroe Islands first took part in European competitions in 1992, after the Faroe Islands Football Association became a member of UEFA in 1990. B36 were drawn against Avenir Beggen in the Cup winners Cup Qualifying round in 1992. They went close but didn't make it through to the first round after a 1-0 loss and a 1-1 at home.