The original production of Sweeney Todd ran from March 1, 1979 to June 29, 1980 at the Original Uris Theatre in New York. It was nominated for 9 Tony Awards, of which it won 8, including Best Musical. A production with George Hearn and Angela Lansbury was televised on September 12, 1982, and the show was revived on Broadway only 9 years after the original production closed, at Circle in the Square, from September 14, 1989 to February 25, 1990.

The original London production opened at the Drury Lane theatre on July 2, 1980 and ran for 157 performances. The show was revived at the Half Moon Theatre on May 1, 1985 where it ran for 33 performances.

Since then, the show has been produced in several countries around the world, and is often performed by opera companies as well. Most recently, a concert version was filmed and broadcast on PBS as well as released on video and DVD.