The past decade has witnessed great success of deep learning technology in many disciplines, especially in computer vision and image processing. However, deep learning-based video coding remains in its infancy. This paper reviews the representative works about using deep learning for image/video coding, which has been an actively developing research area since the year of 2015. We divide the related works into two categories: new coding schemes that are built primarily upon deep networks (deep schemes), and deep network-based coding tools (deep tools) that shall be used within traditional coding schemes or together with traditional coding tools. For deep schemes, pixel probability modeling and auto-encoder are the two approaches, that can be viewed as predictive coding scheme and transform coding scheme, respectively. For deep tools, there have been several proposed techniques using deep learning to perform intra-picture prediction, inter-picture prediction, cross-channel prediction, probability distribution prediction, transform, post-or in-loop filtering, down-and up-sampling, as well as encoding optimizations. According to the newest reports, deep schemes have achieved comparable or even higher compression efficiency than the stateof-the-art traditional schemes, such as High Efficiency Video Coding (HEVC) based scheme, for image coding; deep tools have demonstrated the compression capability beyond HEVC for video coding. However, deep schemes have not yet reached the current height of HEVC for video coding, and deep tools remain largely unexplored at many aspects including the tradeoff between compression efficiency and encoding/decoding complexity, the optimization for perceptual naturalness or semantic quality, the speciality and universality, the federated design of multiple deep tools, and so on. In the hope of advocating the research of deep learning-based video coding, we present a case study of our developed prototype video codec, namely Deep Learning Video Coding (DLVC). DLVC features two deep tools that are both based on convolutional neural network (CNN), namely CNN-based in-loop filter (CNN-ILF) and CNN-based block adaptive resolution coding (CNN-BARC). Both tools help improve the compression efficiency by a significant margin. With the two deep tools as well as other non-deep coding tools, DLVC is able to achieve on average 39.6% and 33.0% bits saving than HEVC, under random-access and low-delay configurations, respectively.The source code of DLVC has been released for future researches.