Blum started acting on stage in the 1970s. In the 1980s, he acted in the movies
Lovesick (1983),
Desperately Seeking Susan (1985),
Just Between Friends (1986),
Crocodile Dundee (1986),
Blind Date (1987), and
The Presidio (1988). Blum won an
Obie Award for his performance as Al in the
Playwrights Horizons production of
Albert Innaurato's play,
Gus and Al, during the 1988–1989 season. On Broadway, he appeared in
Neil Simon's
Lost in Yonkers,
Gore Vidal's
The Best Man, and Richard Greenberg's
The Assembled Parties. In 2013, he appeared as Max in the
Primary Stages production of
The Model Apartment. Blum was on the faculty of
HB Studio in New York City. In 2018, Blum was cast in a recurring role as Ivan Mooney in the former
Lifetime thriller series
You. He regularly acted at
Playwrights Horizons, an
off-Broadway theater in New York City. Blum frequently appeared on
Broadway, including in the revival of
Twelve Angry Men. His recent Broadway credits included
The Assembled Parties, Gore Vidal's
The Best Man—twice—and Neil Simon's
Lost in Yonkers. Blum was active in the
Screen Actors Guild, having served on the New York and national boards. ==Personal life and death==