He was an emeritus professor at the Georgetown University Law Center, and a member of the editorial board of The Nation.
He was educated in New York City's public schools, at Williams College, and earned a doctorate in sociology from Harvard University.
Birnbaum's pedagogical work included the introduction of sociology to the undergraduate curricula at Amherst and Oxford.
A founding member of the editorial board of New Left Review,[citation needed] was active in politics on both sides of the Atlantic He had been an advisor to American trade unions and members of Congress, as well as to a number of social movements and political parties in Europe.
He contributed regularly to a number of publications, including openDemocracy, El País in Spain, and the German daily Die Tageszeitung.