Cobb was a member of the Group Theatre and originated the role of Willy Loman in Arthur Miller's 1949 play Death of a Salesman under the direction of Elia Kazan.

On television, Cobb played a leading role in the first four seasons of the Western series, The Virginian as Judge Henry Garth and the ABC legal drama The Young Lawyers as David Barrett, and was nominated for Primetime Emmy Award for Outstanding Single Performance by an Actor three times.

His parents were Benjamin (Benzion) Jacob, a compositor for The Jewish Daily Forward newspaper, and Kate (Neilecht), a homemaker[6] Interested in acting from a young age, Cobb ran away from home at 16 to try to make it in Hollywood.

He joined Borrah Minevitch's Harmonica Rascals as a musician and had a bit part in a short film featuring the group, but failed to find steady work and eventually moved back to New York.

He starred opposite Elia Kazan in Group Theatre's productions of Clifford Odets' Waiting for Lefty and Golden Boy.

Cobb gained widespread recognition for his portrayal of Willy Loman in the original production of Arthur Miller's play Death of a Salesman under the direction of Elia Kazan.

Miller praised Cobb as "the greatest dramatic actor I ever saw"[9] and, upon his casting, changed a line referring to the physical appearance of the title character, whom the author had originally conceived of as a small man, from "shrimp" to "walrus".

[13] Later that year, he picked up a Best Supporting Actor Oscar nomination for his portrayal of corrupt union boss Johnny Friendly in Elia Kazan's On the Waterfront.

Cobb also appeared as the Medicine Bow, Wyoming owner of the Shiloh Ranch, Judge Henry Garth in the first four seasons (1962–1966), of the long-running NBC Western television series The Virginian (1962–1971).

He reprised his role of Willy Loman in the 1966 CBS television adaptation of Death of a Salesman, which included Gene Wilder, James Farentino, Bernie Kopell, and George Segal.

One of his last television roles was as a stalwart overworked elderly physician still making house calls in urban Baltimore, in Doctor Max, a TV pilot for a potential series that never materialized.

He subsequently appeared alongside British actor Kenneth Griffith in an ABC television documentary on the American Revolution called Suddenly an Eagle, which was broadcast six months after his death.

Following the hearing, he resumed his career and worked with Elia Kazan and Budd Schulberg, two other HUAC "friendly witnesses", on the 1954 film On the Waterfront.

[7] Cobb supported Progressive Party candidate Henry A. Wallace in the 1948 United States presidential election.

[15] Cobb died of a heart attack on February 11, 1976 in Woodland Hills, California at age 64, and was buried in Mount Sinai Memorial Park Cemetery in Los Angeles.