Greb trained very little and was legendary for his carousing and womanizing before fights. Presumably he managed to stay in shape by fighting so often; he is thought to have had some 400 or more bouts during his career. Greb usually fought as a middleweight, but on May 23, 1922, he won the U.S. light heavyweight title, giving Gene Tunney (Tunney, Gene) the only defeat of his career; after the fight, Tunney collapsed in his dressing room, while Greb was left unmarked.

Greb fought most of the great boxers of his time, including Battling Levinsky and Tommy Loughran, and frequently faced men who outweighed him by 40 or more pounds. He won the world middleweight championship in 1923 but lost it three years later to Tiger Flowers in New York City. Greb died following cataract surgery to repair his broken nose, injured in a car accident two weeks previously.It was later confirmed that he had been blind in one eye when he fought many of his later bouts. From 1913 to 1926 Greb fought 294 official bouts, losing only 7 of those fights. He was elected to The Ring magazine's Boxing Hall of Fame in 1955.