An avant-garde taste maker, he founded Grove Press in 1951 and Evergreen Review in 1957, both of which gave him platforms for curating world-class and, in several cases, Nobel prize-winning work by authors including Samuel Beckett (1969), Pablo Neruda (1971), Octavio Paz (1990), Kenzaburō Ōe (1994) and Harold Pinter (2005).

A voracious reader and a resourceful editor, Rosset was the first to publish Beat poets Jack Kerouac, William S. Burroughs and Allen Ginsberg, a who's who of playwrights including Tom Stoppard and Harold Pinter, political biographies like Alex Haley's The Autobiography of Malcolm X, erotic literature like the Story of O, groundbreaking gay fiction by Jean Genet, and banned classics such as Henry Miller's Tropic of Cancer and D. H. Lawrence's Lady Chatterley's Lover.

"To do Lady Chatterley's Lover before Tropic of Cancer would be more acceptable because D.H. Lawrence was a famous writer and revered at many levels," Rosset said in 2009, explaining his tactical reasoning after the fact.

[3][5] Grove Press published Beat Generation writers, including William Burroughs, Allen Ginsberg, Lawrence Ferlinghetti, John Rechy, Hubert Selby, Jr. and Jack Kerouac.

Rosset also purchased the American distribution rights to the Swedish film I Am Curious (Yellow), which had also briefly been banned in Boston, and later found not to be obscene in a Second Circuit Ruling.

"[10] Born and raised in Chicago to a well-to-do Jewish father, also named Barney, who owned a bank, and an Irish Catholic mother, Mary (née Tansey),[5] Rosset attended the progressive Francis Parker School,[11] where he was best friends with Haskell Wexler who went on to become a renowned cinematographer.

[11] In 2002, more than 60 years later, Rosset collected some of his wartime photography for a NYC gallery exhibit that included graphic photos of wounded and dead Chiang Kai-shek soldiers.

[11] Although Rosset's initial ambition was to be a filmmaker like his childhood friend Haskell Wexler,[11] the documentary he produced called Strange Victory about racism in post-World War II America, failed commercially.

Rosset purchased it in 1951 for three thousand dollars, and served as publisher until 1985 when he sold the press to Wheatland Corporation operated by Ann Getty and George Weidenfeld.