She was a touring member of múm for five years from 2003 before launching her solo career and has released three albums to date.

She has collaborated with bands and artists such as Björk, Stórsveit Nix Noltes, Mugison, Slowblow and Skúli Sverrisson.

The success of Við og Við in the US led to Ólöf touring with Blonde Redhead, Jonathan Richman, Björk, The Dirty Projectors and Jeff Mangum, and to her being covered extensively in US publications including Vanity Fair, The New York Times, Village Voice and Time Out New York.

The album was produced by then Sigur Rós members Kjartan Sveinsson and Davíð Þór Jónsson, and featured contributions from Björk, Skúli Sverrisson (Laurie Anderson, Lou Reed), Shahzad Ismaily (Tom Waits, Plastic Ono Band, Bonnie "Prince" Billy), María Huld Markan Sigfúsdóttir (Amiina), and Ragnar.

Produced again by long-time collaborator, Skúli Sverrisson, Sudden Elevation was largely recorded in a late autumn 2011 stint in a seaside cabin in Hvalfjörður, western Iceland.