In 1979, Björk was singing in a band called Exodus with guitarists Ásgeir Sæmundsson and Þorvaldur Bjarni Þorvaldsson, bassist Skúli Sverrisson, and drummer Oddur F. Sigurbjörnsson.

They performed a mixture of pop and punk music and never released any official record, but recorded a cassette demo during a gig at Hólabrekkuskóli which contained the following tracks: two songs by Janis Ian: “Run too Fast, Fly too High” and “The Other Side of the Sun”; two songs by Deep Purple: “Highball Shooter” and “Demon’s Eye”; other tracks were “13–16” by Utangarðsmenn, Jethro Tull's arrangement of J.S.

Tappi Tíkarrass appeared on Rokk í Reykjavík, a TV documentary directed by Friðrik Þór Friðriksson.

Tappi Tíkarrass was one of the 19 bands featured in the film and collaborated with two songs: “Hrollur” and “Dúkkulísur”, both of them sung by Björk and Eyþór with Oddur replacing Guðmundur in drums.

The film was shot in the Westman Islands and Tappi Tíkarrass played on stage two songs “Sperglar” and “Kukl” (better known as “Seiður”), under the supervision of Megas.

Despite the rising interest in this band as Björk developed into an international music artist, the discography of Tappi Tíkarrass has never been reissued and all the original releases are widely unavailable.

Finally, by 1998 record label Spor released Nælur, another compilation which contained the songs “Iltí Ební” and “London”, both of them taken from Bitið fast í vitið.

Tappi Tíkarrass had numerous gigs throughout Iceland when originally formed, and visited UK in spring 1983 (below are listed some of the known performances).