The Frankfurt School is named after the University of Frankfurt, the German university where it was founded. In 1923, Felix Weil and his associates founded the Institute of Social Research at Frankfurt as an interdisciplinary program. As many of the leading thinkers in the school were Jewish, they left Germany with the rise of Hitler, and many ended up in New York. The Frankfurt School very much influenced The New School for Social Research in New York, which played host to many Continental thinkers who were refugees from the Nazis.
Some of the most important figures associated with the school were Max Horkheimer, Theodor Adorno, Herbert Marcuse, Walter Benjamin, Jürgen Habermas, Erich Fromm, and Georg Lukacs. Because of the trauma suffered by both German Jews and other Continental thinkers during the Nazi years, the Frankfurt School was concerned, inter alia, with issues of totalitarianism.
What is now called "critical theory" has its roots in the Frankfurt School's radical critique of earlier philosophical and sociological theories, particularly forms of scientific or logical positivism. Their critique was grounded in the theories of Karl Marx and Friedrich Wilhelm Nietzsche. From Marx, they derived the notion that philosophy and sociology are not some sort of pure, abstract truths but rather rooted in ideologies constructed by economic circumstances, and that the duty of the social theorist is to advocate for social justice. From Nietzsche, they also derived an opposition to notions of the transcendent and an understanding of ideas as radically conditioned.
One important way they extended Marx's work was in their analysis of cultural hegemony, a concern with how cultural production serves to propagate ideology and lead the masses to be complicit in their own oppression, a point especially relevant in light of Hitler's propaganda machine; one of the overwhelming questions for the Frankfurt School was how ordinary citizens could become complicit in something as horrifying as the Holocaust.