The construct of identity is increasingly recognized as a dominant and determining aspect in learning mathematics. While researchers--collectively--theorize identity as situated and negotiated, they also draw attention to the unwieldy nature of the concept that makes it difficult to define and operationalize. The purpose of this paper is to contribute to the conversation on identity in mathematics education by providing a literature review through the lens of a four-part networked identity model configured by Ivanic (1998) in the field of academic writing. Following a short introduction of the meaning of identity as a research construct, the paper discusses Ivanic's four identity-related aspects that include autobiographical identity, discoursal identity, authorial identity, and socioculturally available identities. It then examines research in K-12 mathematics education that focuses on learners' identity through the perspective of Ivanic's model to suggest an instrumental, yet tentative, multi-dimensional framework for exploring identity in mathematics education. The paper concludes with potential trajectories for future research.