Works for dance include music for Dead Souls (Carbone Quatorze Dance Company, directed by Gilles Maheu 1996), and a score for the Royal Winnipeg Ballet's Gita Govinda (2001) based on the 1000-year-old classical Gita Govinda, with choreographer Nina Menon.

In June 2014, Danna was awarded an honorary doctorate by the University of Toronto, for his career achievements in the field of music.

[4] Danna is recognized as one of the pioneers of combining non-Western sound sources with orchestral and electronic minimalism in the world of film music.

This reputation has led him to work with such directors as Atom Egoyan, Deepa Mehta, Terry Gilliam, Scott Hicks, Ang Lee, Gillies MacKinnon, James Mangold, Mira Nair, Billy Ray, Joel Schumacher, and Denzel Washington.

Other films include Dan Scanlon's Onward, Mimi Leder's On the Basis of Sex, Nora Twomey's The Breadwinner, Bennett Miller's Capote and Moneyball and Marc Webb's (500) Days of Summer.