Levine was born in Brooklyn, where his father Harry ran a small clothing factory. His mother, Lena, was a nurse and political activist who had communist sympathies. He began to draw as a child, displaying a precocious talent that, at the age of nine, won him an invitation to audition for an animator's position in Disney's Los Angeles Studios. Levine later studied painting at Pratt Institute, at Temple University's Tyler School of Art in Philadelphia in 1946, and with Hans Hofmann. Immediately following World War II, Levine served in the U. S. Army. After his service, he graduated from Temple with a degree in education and completed his studies at its Tyler School.

A job at Esquire in the early 1960s saw Levine develop his skills as a political illustrator. His first work for The New York Review of Books appeared in 1963, just a few months after the paper was founded. Subsequently, he drew more than 3,800 pen-and-ink caricatures of famous writers, artists and politicians for the publication. Later he drew illustrations that appeared in Esquire (over 1,000 drawings), The New York Times, The Washington Post, Rolling Stone, Sports Illustrated, New York, Time, Newsweek, The New Yorker, The Nation, Playboy, and others.

Levine has received many awards: a Louis Comfort Tiffany Foundation fellowship in 1955; a Guggenheim Fellowship; the Childe Hassam Purchase Prize from the American Academy of Arts and Letters; National Academy of Design prizes, including the Isaac Maynard, Julius Hallgarten and Thomas B. Clarke awards; the George Polk Memorial Award; John Pike Memorial Prize; and the Gold Medal of the American Academy and Institute of Arts and Letters, in 1993. Levine has also been awarded the French Legion of Honor and, in Landau, Germany, the Thomas Nast Award. He is a long-time Academician of the National Academy of Design, New York City.