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Cultural Marxism is a generic term referring to a loosely associated group of Marxists who have sought to apply critical theory to matters of family composition, gender, race, and cultural identity within Western society.
Background and history
“ We are, in Marx's terms, "an ensemble of social relations" and we live our lives at the core of the intersection of a number of unequal social relations based on hierarchically interrelated structures which, together, define the historical specificity of the capitalist modes of production and reproduction and underlay their observable manifestations. — Martha E. Gimenez, Marxism and Class, Gender and Race: Rethinking the Trilogy
According to UCLA professor and critical theorist Douglas Kellner, "Many 20th century Marxian theorists ranging from Georg Lukács, Antonio Gramsci, Ernst Bloch, Walter Benjamin, and T.W. Adorno to Fredric Jameson and Terry Eagleton employed the Marxian theory to analyze cultural forms in relation to their production, their imbrications with society and history, and their impact and influences on audiences and social life."  
Although scholars around the globe have employed various types of Marxist social criticism to analyze cultural artifacts, the two most influential academic institutions upon Western cultural Marxism have been the Institute for Social Research at the University of Frankfurt am Main in Germany (the Frankfurt School), and the Centre for Contemporary Cultural Studies at the University of Birmingham, UK. The latter had been at the center of a resurgent interest in te broader category of cultural Studies.
Frankfurt School and critical theory
Among the key works of the Frankfurt School which applied Marxist categories to the study of culture were Adorno's "On Popular Music," which was written with George Simpson and published in Studies in Philosophy and Social Sciences in 1941, Adorno and Horkheimer's "The Culture Industry: Enlightenment as Mass Deception", originally a chapter in Dialectic of Enlightenment (1947), and "Culture Industry Reconsidered", a 1963 radio lecture by Adorno.
After 1945 a number of these surviving Marxists returned to both West and East Germany. Adorno and Horkheimer returned to Frankfurt in 1953 and reestablished the Institute. In West Germany in the late 1950s and early 1960s, a revived interest in Marxism produced a new generation of Marxists engaged with analyzing matters such as the cultural transformations taking place under Fordist capitalism, the impact of new types of popular music and art on traditional cultures, and maintaining the political integrity of discourse in the public sphere. This renewed interest was exemplified by the journal Das Argument. The tradition of thought associated with the Frankfurt School is Critical Theory.
Birmingham School and cultural studies
The work of the Frankfurt School and of Marxist thinker Antonio Gramsci was particularly influential in the 1960s, and had a major impact on the development of cultural studies, especially in Britain. As Douglas Kellner writes:
Cultural Marxism was highly influential throughout Europe and the Western world, especially in the 1960s when Marxian thought was at its most prestigious and procreative. Theorists like Roland Barthes and the Tel Quel group in France, Galvano Della Volpe, Lucio Colletti, and others in Italy, Fredric Jameson, Terry Eagleton, and cohort of 1960s cultural radicals in the English-speaking world, and a large number of theorists throughout the globe used cultural Marxism to develop modes of cultural studies that analyzed the production, interpretation, and reception of cultural artifacts within concrete socio-historical conditions that had contested political and ideological effects and uses. One of the most famous and influential forms of cultural studies, initially under the influence of cultural Marxism, emerged within the Centre for Contemporary Cultural Studies in Birmingham, England within a group often referred to as the Birmingham School.