Marković is the winner of more than 30 Yugoslavian, Serbian, and international film and theatre awards, the most significant of them being two Pula festival "Zlatna arena" awards, an award for the best director at the San Sebastian Film Festival for the film "Tito and Me", Grand Prix of Americas at the Montreal World Film Festival for the movie "Kordon" and Sterija's Award for the best modern drama text for the theatre play "Turneja". The film version of Turneja won both "Best Film" and "Best Scenario" at the 2009 European Film Festival in Kiev as well as Best Director and the Fipresci awards at the Montreal World Film Festival.

A consistent opponent of the Milosević regime, Marković expressed his political stance in three post-1995 documentary films produced or co-produced with Radio B92: Crazy People (1997), Ordinary Heroes (2000) and Serbia, Year Zero (2001).

Marković is also a professor at Belgrade Faculty of Dramatic Arts and is a member of the European Film Academy in Brussels.