Woods made his mark as a leading man in Videodrome (1983), Once Upon a Time in America (1984) and Oliver Stone's Salvador (1986), which earned Woods a Best Actor Oscar nomination. He continued to make memorable supporting appearances in films such as Casino, Any Given Sunday, Contact and Ghosts of Mississippi (1996), for which he received a Best Supporting Actor Oscar nomination.
Woods regularly takes roles in smaller works from up-and-coming directors, such as Another Day in Paradise (1998), The Virgin Suicides (1999) and Northfork (2003).