She made her Broadway debut in 1963, aged 17, in 110 in the Shade. In 1965 she received wide recognition for playing the title role in the television musical production of Cinderella. She later had starring roles in the Disney musical films The Happiest Millionaire (1967) and The One and Only, Genuine, Original Family Band (1968). In the 1970s, Warren worked mostly on television, receiving a Golden Globe nomination for playing Dana Lambert in the CBS drama series Mission: Impossible (1970–71). In 1978, she won a Golden Globe for Best Actress in a Drama Series for the NBC miniseries Harold Robbins' 79 Park Avenue. In 1983, Warren was nominated for an Academy Award for Best Supporting Actress for playing Norma Cassidy in Victor/Victoria. She received two additional Golden Globe nominations for performances in Songwriter (1984) and Family of Spies (1990). Her other film appearances include Race for the Yankee Zephyr (1981), A Night in Heaven (1983), Choose Me (1984), Clue (1985), Burglar (1987), Cop (1988), Life Stinks (1991), Pure Country (1992), Color of Night (1994), The Limey (1999), and Secretary (2002). Warren was born in New York City, the daughter of Margot (née Verblow), a British-born singer, and William Warren, a real estate agent. She has a brother, Richard Lewis Warren. She attended the Professional Children's School at the age of six and The High School of Music & Art at the age of 13.