She is known for her roles in films such as The Happiest Millionaire, Victor Victoria, Clue, Burglar, Cop, Color of Night and Secretary. She has also had roles in popular TV shows such as Mission: Impossible, Desperate Housewives, Will & Grace, and In Plain Sight.
Warren first came to attention in the 1965 television performance of the Rodgers and Hammerstein musical Cinderella. She won a Golden Globe for the 1977 miniseries Harold Robbins' 79 Park Avenue, and was nominated for an Academy Award in 1982 for Victor/Victoria. In 1985, she played Miss Scarlett in the movie Clue.