Peters created the role of Liesl Von Trapp in the original 1959 Broadway production of The Sound of Music. She received a Tony Award nomination for Best Supporting or Featured Actress in a Musical, which she shared with her sibling castmates. She was married to actor Jon Voight (1962–67), whom she met when he joined the cast as Nazi messenger boy Rolfe, with whom Liesl has a song ("Sixteen Going on Seventeen") and a mutual attraction. She can be heard on the show's cast album, which has sold more than three million copies in the US.

She also appeared as Moll in the revival of Marc Blitzstein's The Cradle Will Rock directed by Howard Da Silva. She appeared on popular television shows of the 1960s and '70s, including Gunsmoke, but worked primarily in the theater, on and off Broadway, and in touring companies.

In Britain, she is probably best known as Cliff Richard's romantic lead in the 1963 film Summer Holiday. On film, she also acted alongside Fabian, James Stewart and Sidney Poitier.

With acting Teacher Sanford Meisner, Peters founded the Meisner Extension at NYU in 1993, where she was Artistic Director and Master Teacher. Teaching the technique away from Manhattan, she has written a book on Meisner.