Carr discovered science fiction fandom in 1949, where he became an enthusiastic publisher of fanzines, which later helped open his way into the commercial publishing world. (He was one of the two fans responsible for the hoax fan 'Carl Brandon' after whom the Carl Brandon Society takes its name.) Despite a long career as a science fiction professional, he continued to participate as a fan until his death. He was nominated five times for Hugos for Best Fanzine (1959–1961, 1967–1968), winning in 1959, was nominated three times for Best Fan Writer (1971–1973), winning in 1973, and was Fan Guest of Honor at ConFederation in 1986.
Though he published some fiction in the early 1960s, Carr concentrated on editing. He first worked at Ace Books, establishing the Ace Science Fiction Specials series which published, among other novels, The Left Hand of Darkness by Ursula K. Le Guin and Rite of Passage by Alexei Panshin.
After conflicts with Ace head Donald A. Wollheim, he worked as a freelancer. He edited an original story anthology series called Universe, and a popular series of The Best Science Fiction of the Year anthologies that ran from 1972 until his death in 1987. He also edited numerous one-off anthologies over the same time span. He was nominated for the Hugo for Best Editor thirteen times (1973–1975, 1977–1979, 1981–1987), winning twice (1985 and 1987). His win in 1985 was the first time a freelance editor had won.
Carr taught at the Clarion Workshop at Michigan State University in 1978, where his students included Richard Kadrey and Pat Murphy.
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