Among her many collaborations, she has: led a trio with John Hébert [de] and Ches Smith, and a quintet with the addition of Jon Irabagon and Jonathan Finlayson; recorded duo albums with violist Jessica Pavone; and recorded several albums with bassist Michael Formanek and drummer Tomas Fujiwara [de] under the band name Thumbscrew.

[2] She initially enrolled in Wesleyan University to study biology, but dropped her prospective major after sitting in on one of saxophonist Anthony Braxton's music classes.

[6] In 2013, the trio of Halvorson, bassist Michael Formanek, and drummer Tomas Fujiwara [de] recorded the first of several albums as the band Thumbscrew.

[7][8] NPR called Halvorson's 2015 solo album Meltframe "category-exploding", and its 2015 Jazz Critics Poll named the record 7th-best of the year.

[3] The album Code Girl was Halvorson's first attempt at writing lyrics for her original works, which are sung by Amirtha Kidambi and inspired by the songwriting of Robert Wyatt and Elliot Smith.

The album received an 8.1 rating from a Pitchfork review, explaining, "The pleasure of this kind of text comes from the way it invites active listening as a means of interpretation.

In speaking with PostGenre, Halvorson noted that she's "never really felt like I had to stick with a particular style or idea... From [Anthony Braxton], I learned that it was normal to take such a broad approach.