In 1967, John Rex and Robert Moore published an influential book on ethnic housing inequality in Birmingham, titled Race, Community and Conflict. The book presented a theory about classes formed in the housing market, inspired by a particular reading of Max Weber's ideas about class. The basic idea of the housing class is that people's relation to the means of housing is a class-forming factor that is not reducible to their relation to the means of production. This paper presents the original housing class theory and its revision by Peter Saunders, property class theory, and criticisms of the two theories. Since the 1980s, both theories have disappeared from housing research. In the 2020s, the basic idea of the housing class was revived in Lisa Adkins' and her co-authors' asset class theory. This paper discusses the history of the idea of the housing class and its contemporary relevance. It also raises questions about the conceptualization of class and housing inequality.