In recent years, research in higher education physics has paid increased attention to identity issues. In this critical review of the literature, we query research projects with the question “what is the problem represented to be” in order to elicit a discussion of the state of research on identity in university physics, and to discuss possible lessons to be learned for future developments. In particular, we outline four “problematizations” implied by how identity is conceptualized and used in research papers using identity: (1) students fail to develop a physics identity; (2) underrepresented students do not develop enough of a physics identity; (3) normative physics identities impede equal participation, and; (4) normative physics identities have consequences for what physics knowledge is produced, and the role of physics in society. With examples from the literature and our own research, we highlight the implications of the various ways in which identity has been approached. We discuss the risks of some approaches representing students as “deficient” without problematizing physics itself, and highlight the under-explored potential of analysing identities, knowledge and social justice together. With this, we aim to provide a background for critical developments of identity studies in physics education.