Greenberg was ranked fifth in the US in singles in 1943 and 1944 and also in the top 10 in three other years.
Greenberg won the Illinois State high school singles titles in 1936 and 1937 while at Lane Technical College Prep High School in Chicago, where he was valedictorian.
Greenberg won the Illinois State Championships nine times.
Greenberg was captain of the Northwestern University tennis team and became that school's first Big Ten Conference singles champion when he won the title in 1940. He repeated in 1941 and won the Big Ten doubles championships in 1940 (with Jerry Clifford), 1941 (with Gene Richards), and 1942 (also with Richards). Greenberg's three doubles titles still rank first all-time in Big Ten history. He led the Northwestern Wildcats to the Big Ten team championships in 1940 and 1942.
Greenberg won the City of Chicago Championship in 1939 and the U.S. Men's Clay Court Championships in 1942 and 1943.
Greenberg was also a singles quarterfinalist at the U.S. Championships in 1942, 1943, 1944, and 1945.
In 1943 at the tournament in Cincinnati, Ohio, Greenberg reached the singles and doubles finals but lost the singles final to future International Tennis Hall of Fame inductee Bill Talbert. He lost the doubles final to Talbert and partner Alvin Bunis. Greenberg had partnered with Joe Scherr to reach the final.
Halls of Fame
Greenberg has been inducted into:
- the Chicago Jewish Sports Hall of Fame (1982),
- the United States Tennis Association/Midwest (formerly Western Tennis Association) Hall of Fame (in 1990),
- the Northwestern University Athletic Hall of Fame (2000), and
- the Chicago Tennis Hall of Fame (2004)
Greenberg was the son of Jacob and Sylvia Greenberg and married the late Wanda Henderson in 1952.
Greenberg's death resulted from complications of Parkinson's disease.