Although she has become a popular performer at Canadian folk festivals, such asFolk on the Rocks in 2005, she is best known both in Canada and internationally for her collaborations with Björk, including concert tours and the 2004 albumMedúlla. She has also performed with the Kronos Quartet and Shooglenifty and featured on the Aboriginal Peoples Television Network.
In 2005, her CD entitled Sinaa (Inuktitut for "edge") was nominated for five awards at the Canadian Aboriginal Music Awards. At the ceremony on 25 October 2005, the CD won awards for Best Producer/Engineer, Best Album Design and Tagaq herself won the Best Female Artist award.
Her most recent album, Auk/Blood (ᐊᐅᒃ Inuktitut syllabics) features collaborations with Mike Patton, among others. In 2011, she released a live album titled Anuraaqtuq. It was recorded during Tagaq's performance at the Festival International de Musique Actuelle in Victoriaville.