Oppression is a form of injustice that occurs when one social group is subordinated while another is privileged, and oppression is maintained by a variety of different mechanisms including social norms, stereotypes, and institutional rules. A key feature of oppression is that it is perpetrated by and affects social groups. In this article I show that because of the central role that groups play in theories of oppression, those theories face significant, and heretofore mostly unrecognized, metaphysical problems. I then identify resources from analytic metaphysics that can be used to address these problems. I show that, although we should not be pessimistic about the prospects for a viable theory of oppression, it will take serious metaphysical work to develop a plausible ontology of oppression, and existing theories have for the most part failed to respond to this challenge.