In the early 1920s, a formidable array of intellectual talent coalesced into a group that called themselves the Institut fur Sozialforschung (the Institute for Social Research). They would later come to be known more simply as the Frankfurt School. Consisting mostly of assimilated German Jews, they had a truly impressive body of interests, running from sociology, sinology, philosophy, Marxism, musicology, psychology, and psychoanalysis. Max Horkheimer and Theodor Adorno are probably most affiliated with the first generation of the school, but it also included Herbert Marcuse, Erich Fromm, Leo Lowenthal, Paul Lazarsfeld, and Franz Neumann, many of whom are still read today.
But when one does hear the words "Frankfurt School" today, their influence on Marxism is perhaps what most immediately comes to mind. The members thought that the German Social Democratic Party was spineless and ineffective, but equally thought that the Communist party was too hard-lined and ideological. Because of this, their academic work paved a middle course between the bourgeois politics of the Social Democrats and the sclerotic, obsolescent, vulgar Marxism that they perceived in Germany, and which was soon to all but disappear.
Martin Jay uses this book as an opportunity to write a multi-person biography of many of the figures above, interlarded with the objective, measured perspective that I've come to know Jay for. (I've also read his "Songs of Experience: Modern American and European Variations on a Universal Theme," which is a philosophical history of experience over the last four hundred years or so, and which I have also reviewed for this site.) He discusses the major work which they produced, including their analysis of Nazism, aesthetic theory and Adorno's devastating critique of mass culture, and the later more empirical work that came out after World War II. In the last chapter, some of the contributions of Walter Benjamin, a figure more peripherally related to the school but still extraordinarily important in his own right, are more fully fleshed out. In school, I read Benjamin's "Art in the Age of Mechanical Reproduction" (which I'm sure that every student in a philosophy of art course is made to read), and found that it completely changed some of my assumptions about aesthetic experience. I have several other volumes of Benjamin's work, including one of media criticism, and Jay's book has made me much more curious to pick those up.
If there is one complaint that I could level against the book, it would be that Jay pays almost equal attention to everyone, even those figures that few people really read these days. For whatever reason, I thought "history of the Frankfurt School" might mean "a detailed discussion of Horkheimer and Adorno," with maybe a little Marcuse or Benjamin tossed in for good measure. But he really tells the entire history of the Institute itself, including how it was funded and the minor figures that no one really except for perhaps academic specialists read anymore (like Neumann and Lazarsfeld). If you're looking for a book that gives a more straightforward account on the major ideas of critical theory and its continuing interdisciplinary influences, this isn't really the book that you're looking for - which is what this book seemed to be - this isn't really the book for you. If this is what you're more interested in I've heard, though I can't confirm since I haven't read them, that the Very Short Introduction's book on the group by Stephen E. Bronner or Thomas Wheatland's "The Frankfurt School in Exile" might be more appropriate.