Greenwich's songs were the basis of the 1985 Broadway revue Leader of the Pack, which earned a Tony Award nomination for Best Musical. She also appeared in the production, alongside Patrick Cassidy, Dinah Manoff, Annie Golden, Jasmine Guy, Darlene Love, and other stars.
In addition to the song "Leader of the Pack," Greenwich wrote such iconic hits as "Be My Baby," "Chapel of Love," and "Christmas (Baby Please Come Home)." In 1991, she and Jeff Barry, her former husband and songwriting and producing partner, were inducted into the Songwriters' Hall of Fame.
Greenwich's songs were also featured in three other Broadway revues: Uptown, It's Hot!, Andre De Shields' Harlem Nocturne, and Rock 'n' Roll! The First 5,000 Years.
During her career as writer and producer, Greenwich also worked with such top talents as Phil Spector, Neil Diamond, Frank Sinatra, Lesley Gore, Bobby Darin, Nona Hendryx, and Cyndi Lauper.
She is survived by her sister, Laura Weiner. Donations can be made to the VH1 Save the Music Foundation.