The Maryland native made his stage debut as Eugene Gant in a 1963 production of "Look Homeward, Angel" at the Barter Theatre in Abingdon, Virginia. He toyed with the idea of becoming an English professor, but decided, instead, to give New York theatre a try and migrated to Manhattan in 1967. Roles in regional theater followed before he made his Off-Broadway debut in "A Scent of Flowers" (1969). Glover won a Drama Desk Award for his work in "The Great God Brown" (1972) and that same year, he made his Broadway debut in "The Selling of the President". Since then, he has performed on stage in between a busy TV and film career, appearing both in New York and Los Angeles as well as frequently at the Long Wharf Theatre and Yale Rep. In 1994, Glover originated the dual role of John and James Jeckyll, gay twin brothers, one with AIDS, in Terrence McNally's "Love! Valour! Compassion!", a role that earned him a Tony Award (and which he recreated in the 1997 film version) Glover was back on the New York stage in the spring of 1996 playing a religious hypocrite in "Tartuff: Born Again" at the Circle in the Square Theatre, an adaptation of the Moliere comedy.
His film career began in 1973 with a small role in "Shamus". Glover received a lot of attention for his one scene in "Julia", in which Jane Fonda pushes a table over on top of him after he suggests that she and the title character are lesbian lovers. Since then, Glover has most frequently been cast as cold sons-of-bitches, such as in "52 Pick-Up" (1986). Other similar roles followed: the sly CIA agent in "White Knights" (1985); an opportunistic TV executive in "Scrooged" (1988); a murderous stepfather in "Masquerade" (1988); and an intelligent manipulator in "The Chocolate War" (1989). Even in a comedic turn in "Gremlins 2: The New Batch" (1990), he was a sleazy, greedy real estate baron. Glover was also a hired killer in "Night of the Hit Man" (1994).
TV roles have not offered sweet guys, either. Glover made his TV-movie debut in "The Face of Rage" (ABC, 1983). He displayed his versatility as a man dying of AIDS who befriends Aidan Quinn in "An Early Frost". While the role was sympathetic, the character also had a vicious, cutting wit. Even as General Charles Lee in the 1984 ABC miniseries "George Washington", Glover could not be trusted to follow orders. He starred with Corbin Bernsen in "Breaking Point" (TNT, 1989), playing a genius--but a Nazi genius. In perhaps his most psychotic role to date, Glover was Charles Rothenberg, the man who burns his own son practically to death rather than let his mother have him in "David" (ABC, 1988). For Showtime, Glover was a military prosecutor who sets out to prove that an African American West Point cadet tried to harm himself and was not attacked by racist whites in "Assault at West Point" (1994). In 1996, he made a guest appearance on "Remember WENN", the first sitcom from American Movie Classics. Glover also cut a marvelously sinister presence as the devil in the short-lived Fox drama "Brimstone" (1998-99).