Now, as to the work: the Frankfurt school were dissident Marxists, severe critics of capitalism who believed that a narrow selection of Marx's ideas were being repeated uncritically by those who claimed to follow his lead, usually in defense of the Communist Party. They took up the task of distinguishing what might be useful in Marx when applied to social conditions he had never seen. They drew on other schools of thought to fill in what they thought were omissions in Marx's. Max Weber was a principal influence, but Herbert Marcuse , for example, sought to combine the views of Marx? and Freud.
The Frankfurt school was literally a school, a place where individuals taught and learned. There is no one method, ambition, or conclusion shared by all of them.
However, there is a broad emphasis on criticizing the CULTURE of capitalism (and orthodox communism). The title of one book, Leo Lowenthal's LITERATURE, POPULAR CULTURE, AND SOCIETY, gives an idea of their interests. In Habermas, the work becomes focussed on the question of what cultural conditions are necessary to make good intellectual work possible--or, more pessimistically, how far economic interests and political authority can corrupt science and philosophy.
This general emphasis on culture as a product of economic systems has influenced literary historians, film critics, historians of science, and so forth. The search for useful ideas from other fields has also been imitated. Therefore, the term critical theory now is used loosely to group all sorts of work--Structuralism, the anti-structuralist views known as Postmodernism, and so on. See Cultural movement.
See [Walter Benjamin]?, Theodor Adorno, Herbert Marcuse, Max Horkheimer, Jurgen Habermas, Max Weber.