After a widely praised performance as a teenager in Picnic, Strasberg originated the title role in the Broadway production of The Diary of Anne Frank and was nominated for a Tony Award at the age of 18. Strasberg became the youngest Actress to star on Broadway with her name above the marquee title. In 1955, she appeared twice on the cover of Life (July 11, 1955 issue; November 11, 1955 issue) and soon after on the cover of Newsweek (December 19, 1955 issue). She later starred in the Italian Holocaust film Kapò which was nominated for an Academy Award as best foreign film of 1960.
From the 1960s through the 1980s, she guest-starred in such television series as The Virginian, The Invaders, Bonanza, The F.B.I., Breaking Point, Burke's Law, The Streets of San Francisco, Night Gallery, McCloud, Alias Smith & Jones, The Big Valley, Remington Steele, and The Rockford Files ("The Countess" (1974), "Bad Deal In The Valley" (1976)), Mannix and The Love Boat. She lived in Italy in the early 1960s, where she was often called 'La Strasberg'. In 1993, she was a jury member for the 43rd Berlin International Film Festival.
On September 25, 1965, Strasberg married actor Christopher Jones, with whom she had appeared in an episode of The Legend of Jesse James. Their daughter, Jennifer Robin, was born six months later. The couple divorced in 1968.
In the mid 1990s, Strasberg was diagnosed with breast cancer. She died of the disease at her home in New York City on January 21, 1999, at the age of 60.