Grandfather Edward Bennett Close was once married to cereal heiress Marjorie Merriweather Post, the mother of actress Dina Merrill. Glenn is also a second cousin of Brooke Shields, and is distantly related to Princess Diana.
Father, a physician, opened a clinic in Congo when she was 13.
Made her Broadway debut (in a starring role) in the 1974 Phoenix Theatre Company production of William Congreve's Love for Love.
Big-screen debut was in the role of Robin Williams' mother Jenny Field in the 1982 film The World According to Garp.