Face anti-spoofing (FAS) has lately attracted increasing attention due to its vital role in securing face recognition systems from presentation attacks (PAs). As more and more realistic PAs with novel types spring up, early-stage FAS methods based on handcrafted features become unreliable due to their limited representation capacity. With the emergence of large-scale academic datasets in the recent decade, deep learning based FAS achieves remarkable performance and dominates this area. However, existing reviews in this field mainly focus on the handcrafted features, which are outdated and uninspiring for the progress of FAS community. In this paper, to stimulate future research, we present the first comprehensive review of recent advances in deep learning based FAS. It covers several novel and insightful components: 1) besides supervision with binary label (e.g., '0' for bonafide vs. '1' for PAs), we also investigate recent methods with pixel-wise supervision (e.g., pseudo depth map); 2) in addition to traditional intra-dataset evaluation, we collect and analyze the latest methods specially designed for domain generalization and open-set FAS; and 3) besides commercial RGB camera, we summarize the deep learning applications under multi-modal (e.g., depth and infrared) or specialized (e.g., light field and flash) sensors. We conclude this survey by emphasizing current open issues and highlighting potential prospects.