Social Virtual Reality (social VR or SVR) provides digital spaces for diverse human activities, social interactions, and embodied face-to-face encounters. While our digital bodies in SVR can in general be of almost any conceivable appearance, individualized or even personalized avatars bearing users’ likeness recently became an interesting research topic. Such digital bodies show a great potential to enhance the authenticity of social VR citizens and increase the trustworthiness of interpersonal interaction. However, using such digital bodies might expose users to privacy and identity issues such as identity theft: For instance, how do we know whether the avatars we encounter in the virtual world are who they claim to be? Safeguarding users’ identities and privacy, and preventing harm from identity infringement, are crucial to the future of social VR. This article provides a systematic review on the protection of users’ identity and privacy in social VR, with a specific focus on digital bodies. Based on 814 sources, we identified and analyzed 49 papers that either: 1) discuss or raise concerns about the addressed issues, 2) provide technologies and potential solutions for protecting digital bodies, or 3) examine the relationship between the digital bodies and users of social VR citizens. We notice a severe lack of research and attention on the addressed topic and identify several research gaps that need to be filled. While some legal and ethical concerns about the potential identity issues of the digital bodies have been raised, and despite some progress in specific areas such as user authentication has been made, little research has proposed practical solutions. Finally, we suggest potential future research directions for digital body protection and include relevant research that might provide insights. We hope this work could provide a good overview of the existing discussion, potential solutions, and future directions for researchers with similar concerns. We also wish to draw attention to identity and privacy issues in social VR and call for interdisciplinary collaboration.