HAM’s first album was Hold, a controversial record which received no radio airtime. The band’s attempt to get into the big league began when they warmed up for The Sugarcubes in five concerts in 1988. The following year they released the album Buffalo Virgin with One Little Indian records and held several concerts in New York. The album Pleasing the Pirahna was recorded in 1990 but was never released—supposedly another album by the name Pimpmobile was also recorded but remains unreleased.

In 1991-1992, the band participated in the making of the film Sódóma Reykjavík, with singer and guitarist Sigurjón Kjartansson writing most of the soundtrack. HAM’s participation in the making of this cult Icelandic classic played a significant part in the band’s later notoriety.

The album 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 recording was subsequently 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, when it was clear that the German metal band Rammstein would be holding a concert in Iceland that summer. It was rumoured that Sigurjón had spoken of HAM reuniting for a concert if Rammstein were to visit Iceland on tour. The band played in the Gaukur á Stöng bar on June 14, 2001 and then again on June 15, with 5500 people in attendance. The Gaukur á stöng concert was later released as the live album Skert flog.

HAM was to participate in the music festival Reykjavík Rokkar in the summer of 2006 along with The Darkness and Motörhead. The festival was cancelled due to disappointing ticket sales, but HAM instead performed in the NASA club in downtown Reykjavík on June 29 to a packed house. On October 28 the same year HAM performed at a north atlantic music festival in Copenhagen with bands from Denmark, Greenland and the Faroe Islands.

On September 6, 2007, Ham were the final band to play at the ‘Minifestival’ benefit concert at Iðnó, Reykjavík. Their participation was not advertised until the night of the event.

In July 2008, HAM were the closing act to the Icelandic heavy metal festival “Eistnaflug”, where they performed a new song.

HAM participated in the 2011 “Eistnaflug” festival as the closing act and later that year they released their first new album in 16 years, Svik, harmur, dauði (English: Betrayal, Tragedy and Death).