Recent years have seen remarkable progress in deep learning powered visual content creation. This includes 3D-aware generative image synthesis, which produces high-fidelity images in a 3D-consistent manner while simultaneously capturing compact surfaces of objects from pure image collections without the need for any 3D supervision, thus bridging the gap between 2D imagery and 3D reality. The 3D-aware generative models have shown that the introduction of 3D information can lead to more controllable image generation. The task of 3D-aware image synthesis has taken the field of computer vision by storm, with hundreds of papers accepted to top-tier journals and conferences in recent year (mainly the past two years), but there lacks a comprehensive survey of this remarkable and swift progress. Our survey aims to introduce new researchers to this topic, provide a useful reference for related works, and stimulate future research directions through our discussion section. Apart from the presented papers, we aim to constantly update the latest relevant papers along with corresponding implementations at https://weihaox.github.io/awesome-3D-aware-synthesis.