Greek, composed with the encouragement of Hans Werner Henze and first performed in 1988 at the Munich Biennale, is based on Steven Berkoff's adaptation of Oedipus Rex.

[5] He has composed song cycles for a number of celebrated singers including Sarah Connolly, Gerald Finley and Allan Clayton.

Other choreographers that have made ballets to Turnage's works include Heinz Spoerli (Zurich Ballet 2007 and Staatsballet Berlin 2012), Ashley Page (Rambert Dance Company 2013), Jorma Elo (Hubbard Street Dance Chicago 2007) and Gregor Zollig (Tanztheater Bielefeld 2006).

Between 2006 and 2010, Turnage was a co-composer-in-residence of the Chicago Symphony Orchestra, a position he held alongside Argentinian composer Osvaldo Golijov.

[7][8][9] In January 2025 Turnage was the castaway for BBC Radio 4's Desert Island Discs, where his choices included "Notre Dame des Jouets" by Oliver Knussen, "Blue in Green" by Miles Davis and "Living for the City" by Stevie Wonder.

In the same programme he spoke about volunteering regularly at a food bank, and about working on music projects with prisoners.