Jón was a well-known comedian and actor starting in the 1990s, including teaming with Sigurjón Kjartansson as the duo Tvíhöfði on radio and television.

[6] Jón was misdiagnosed with severe intellectual disability as a child and was treated between the ages of five and seven at the children's psychiatry ward at the State Hospital at Dalbraut, Reykjavík.

[9] During the 1980s, he and his future wife, Jóhanna "Jóga"[10] Jóhannsdóttir, became acquainted with the members of the Reykjavík-based alternative rock band the Sugarcubes, including Björk Guðmundsdóttir and Einar Örn Benediktsson.

His graduation work was his own performance of the ancient Icelandic poem Völuspá from the Poetic Edda[12] In 1994, Jón teamed up with Sigurjón Kjartansson to form the radio duo Tvíhöfði.

He worked as a creative writer and actor at the Icelandic advertising agency EnnEmm, producing several popular TV ads.

[citation needed] Jón ended up defeating the centre-right Independence Party-led municipal government of Hanna Birna Kristjánsdóttir, which came as "a shock" to Icelandic Prime Minister Jóhanna Sigurðardóttir.

[16] His political platform included promises of "free towels in all swimming pools, a polar bear for the Reykjavík zoo, all kinds of things for weaklings, Disneyland in the Vatnsmýri area, a 'drug-free' Althing by 2020, sustainable transparency, tollbooths on the border with Seltjarnarnes, to do away with all debt, free access to Hljómskálagarðurinn (orchestral rotunda park).

[19] Ultimately, his Best Party entered into a coalition with the social-democratic Social Democratic Alliance (Samfylkingin) as its junior partner to govern Reykjavík.

[20][21] As mayor, he appeared at the 2010 Gay Pride parade as a drag queen,[22][23] posted a video holiday greeting wearing a Darth Vader mask and a Santa Claus cap,[24] and suggested a merger with neighboring municipality Kópavogur.

[31] In January 2015 Jón joined the Center for Energy and Environmental Research in the Human Sciences (CENHS) at Rice University as their first writer in residence.

[32][33] After the incumbent President of Iceland, Ólafur Ragnar Grímsson, announced on 1 January 2016 that he would not run in the upcoming presidential election, it was speculated that Jón would put forward his candidacy.