A graduate of Carnegie Mellon University, Breverman has exhibited in New York, Toronto, London, Amsterdam, Oslo, Paris, Bologna, Moscow, Basel, Barcelona, Crakow, Belgrade, Rome, Milan, Vienna, Honolulu, Tokyo, Caracas, and Rio de Janeiro. He has had eighty-four solo exhibitions. His works are in the collections of the Museum of Modern Art, the Metropolitan Museum, the Whitney Museum and the Jewish Museum and the Library of Congress, Washington, D.C.; The British Museum, London; and the Israel Museum, Jerusalem.

He received grants and awards from the Tiffany Foundation in 1962, the Netherlands Government in 1965, the New York State Council on the Arts (CAPS) in 1972, the National Endowment for the Arts in 1974 and 1980, and the American Academy/National Institute of Arts and Letters, New York in 1980 and 1981.

Representing the U.S., he participated in International Print Biennales in England, Norway, Spain, Taiwan, China, Japan, Finland, Poland, Bulgaria, Italy, Germany, Egypt, Thailand, and Turkey. Breverman has taught and been a visiting artist at Ohio University, Illinois State, Michigan, Indiana, Skidmore, Maryland Institute, William and Mary, Oxford University’s Ruskin School, England, Pont Aven School of Art, France, and Jagiellonian University, Poland.

A member of the National Academy since 1993, he received the Ralph Fabri Prize in 1993; the Leo Meissner Prize in 1995; the 1st Benjamin Altman Figure Painting Prize in 1999 and the Adolph and Clara Obrig Prize in Painting in 2001. In 2003 he received the Distinguished Teaching of Art Award from the College Art Association. He is SUNY Distinguished Professor of Art at the University at Buffalo.