Gudnadóttir began playing cello as a child, entered the Reykjavík Music Academy and then moved on to musical studies/composition and new media at the Iceland Academy of the Arts and Universität der Künste Berlin.
Hildur has released four critically acclaimed solo albums: Mount A (2006), Without Sinking (2009), Leyfðu Ljósinu (2012) and Saman (2014). Her records have been nominated a number of times for the Icelandic Music Awards. Hildur’s albums are all released on Touch.
She has composed music for theatre, dance performances and films. The Icelandic Symphony Orchestra, Icelandic National Theatre, Tate Modern, The British Film Institute, The Royal Swedish Opera in Stockholm and Gothenburg National Theatre are amongst the institutions that have commissioned new works by Hildur. She was nominated for the Nordic Music Council Prize as composer of the year 2014.
Among others Hildur has performed live and recorded music with Skúli Sverrisson, Jóhann Jóhannsson, múm, Sunn O))), Pan Sonic, Hauschka, Wildbirds & Peacedrums, Ryuichi Sakamoto, David Sylvian, The Knife, Fever Ray and Throbbing Gristle.
In 2018 Hildur was nominated for a Discovery of the Year Award at the World Soundtrack Academy in Gent and received several prestigious awards, including the Asia Pacific Screen Award for Best Score (Mary Magdalene) and Best Score at the Beijing International Film Festival for Journey’s End.