Greenberg took a doctorate in Political Science in 1969, and has taught at the University of Wisconsin - Green Bay since 1975. His first anthology was Political Science Fiction (1974, with Patricia Warrick), intended to be used as a teaching guide, then continuing with a sequence of educational anthology titles under the series name Through Science Fiction. In the late 70s Greenberg began partnering with Joseph D. Olander on more conventional SF anthologies. Early in his career, Greenberg was sometimes confused with Martin Greenberg the publisher of Gnome Press, but the anthologist has stated (at science fiction conventions, and in some of his anthologies) that they are no relation.

In the 1990s he has also written some books in corporation of Tom Clancy (powerplays).

He shared the 2005 Prometheus Special Award with Mark Tier for the anthologies Give Me Liberty and Visions of Liberty.

Greenberg typically teams up with another editor, splitting the duties of story selection, editing, copyright searches, and the handling of author royalties. Major partners include Isaac Asimov (127 anthologies), Charles G. Waugh, Jane Yolen, and Robert Silverberg.

Asimov suggested that he call himself "Martin H. Greenberg" or "Martin Harry Greenberg" to distinguish him from Martin Greenberg, who also worked in the same general field.

In 2009, he was the recipient of one of the first three Solstice Awards presented by the SFWA in recognition of his contributions to the field of science fiction.

• The Dog Star (2004)
• Once Upon a Galaxy (2002)
• Past Imperfect (2001)
• The Greatest Stories (1996)
• Dark Love (1995)
• The Further Adventures of The Joker (1990)
• Foundation's Friends (1989)
• Young Extraterrestrials (1984)
• 2000 (1982)
• The Science Fictional Solar System (1979)
• Dawn of Time (1979)

Short story anthologies edited by Martin H. Greenberg

• Werewolves (1988, with Jane Yolen)
• Nightmares on Elm Street: Freddy Krueger's Seven Sweetest Dreams (1991)
• Xanadu (1992, with Jane Yolen)
• Xanadu 2 (1993, with Jane Yolen)
• Xanadu 3 (1994, with Jane Yolen)