His decision proved wise: In 1993, Wright was cast as Roy Cohn's flamboyant nurse in "Angels in America, Perestroika," a role that netted the actor a Tony Award and an Emmy when he reprised the part in the HBO miniseries. More accolades followed for his performance as the title character in Basquiat (1996).
Other notable films for Wright include Ali (2001), The Manchurian Candidate (2004), Broken Flowers (2005) and the James Bond saga Casino Royale (2006).