After graduating from New York University in 1933, majoring in writing, Kramer accepted an internship in Hollywood as a production assistant. He worked as a set p.a. at several studios from 1933 onward and eventually worked at Universal in the early 1940s as part of the swing gang in the art department.
Biography in: John Wakeman, editor. "World Film Directors, Volume Two, 1945-1985". Pages 538-544. New York: The H.W. Wilson Company, 1988.
Directed 14 different actors in Oscar-nominated performances: Tony Curtis, Sidney Poitier, Theodore Bikel, Cara Williams, Spencer Tracy, Maximilian Schell, Judy Garland, Montgomery Clift, Oskar Werner, Michael Dunn, Simone Signoret, Katharine Hepburn, Cecil Kellaway and Beah Richards. Hepburn and Schell won Oscars for their performances in one of Kramer's movies.
Has a street in Berwick, Australia where part of On the Beach (1959) was filmed, named in his honour - Kramer Drive.
Was to name his child after Spencer Tracy, but when the baby turned out to be a girl, he named her after Katharine Hepburn. Hepburn was also her godmother.