HAM's first album Hold (EP) was released in 1988. The following year their first LP, Buffalo Virgin, was released with One Little Indian records.
In 1991-1992, the band took significant part in the making of the film Sódóma Reykjavík.
Saga rokksins was released in 1993, and on June 4, 1994, the band held its last concert in the now defunct night club Tunglið in downtown Reykjavík. The live concert recordings were released as the album Lengi lifi. In 1995, the band's remaining studio recordings were released as the album Dauður hestur (Equus Mortus).
HAM did not perform again until 2001, where they played 3 concerts, the recordings from that reformation becoming the live album Skert flog.
In 2011 HAM released their first new studio album in 16 years, Svik, harmur, dauði. In 2017 they released Söngvar um Helvíti Mannanna.
HAM created a soundscape for artist Hrafnhildur Arnardottir, aka Shoplifter, for her show at the Venice biennale in 2018. The first single from those recordings, Haf trú, has just been released on streaming services.