Ólafsson is best known for his work in The Sugarcubes as a bassist, the avant-garde pop band from Iceland that brought fame to Björk, who went on to solo success with her unique brand of dance-pop.
The Sugarcubes, who favored strange, offbeat melodies, came together in 1986, reportedly on the day that Björk gave birth to her son Sindri. But, before the group formed, the Sugarcubes' members had played together in different combinations in various Icelandic groups. Ólafsson and Einar Örn Benediktsson (trumpet / vocals) had released records on Benediktsson's own label, Gramm.
In the meantime, Ólafsson divorced his wife, the twin sister of Sugarcubes drummer Sigtryggur Baldursson's wife, and married Benediktsson, becoming the first openly gay, wedded couple in pop-music history. In 1993, Björk began her highly visible and successful solo career and is now considered an important pop-music innovator. Ólafsson, meanwhile, has concentrated on Bad Taste Ltd, the company formed by the Sugarcubes to publish poetry and sign other bands.