A classically trained cellist, she has played and recorded with the bands Pan Sonic, Throbbing Gristle, Múm, and Stórsveit Nix Noltes, and has toured with Animal Collective and Sunn O))).

Hildur has gained international recognition for her film and television scores, including Journey's End (2017), Mary Magdalene (2018), Sicario: Day of the Soldado (2018), Todd Field's Tár and Sarah Polley's Women Talking (both 2022).

[12] She composed the score to the 2019 film Joker, starring Joaquin Phoenix and Robert De Niro, and directed by Todd Phillips, for which she won the Premio Soundtrack Stars Award at the 76th Venice International Film Festival and the Golden Globe Award for Best Original Score,[13] becoming the first solo woman composer to win in this category.

[5][20] She is married to Sam Slater, an English composer, music producer and sound artist, with whom she collaborated on multiple projects including Chernobyl and Joker.

[4][21][22][23] She also used to share a studio with fellow composers Dustin O'Halloran and the late Jóhann Jóhannsson, the latter being a frequent collaborator, while residing in Berlin.