He then began his career onstage at the Leikfélag Reykjavíkur, Reykjavik's premier theatre company, where he appeared in productions as: John Steinbeck's' The Grapes of Wrath, William Shakespeare's Hamlet, Molière's Tartuffe, Anton Chekhov's Platonov and Birgir Sigurðsson's Degi vonar.
[2] Þröstur's first film role came in the 1986 Hilmar Oddsson-directed drama Eins og skepnan deyr (English release title: The Beast).
He is possibly best recalled internationally for his roles in Baltasar Kormákur's 2000 romantic comedy 101 Reykjavík, opposite Spanish actress Victoria Abril, Kormákur's 2002 drama Hafið (English release title: The Sea), 2002's United States/Icelandic coproduction of No Such Thing, a bilingual fantasy starring Sarah Polley, Helen Mirren and Julie Christie, and Dagur Kári's 2003 drama Nói albínói (Nói the Albino).
In 2008, Þröstur won Iceland's Edda Award for Best Supporting Actor for his role in the Baltasar Kormákur directed drama Brúðguminn.
[5][6] On 7 July 2015, a fishing vessel he was working on, Jón Hákon BA 60, capsized and sank close to Aðalvík.