Characterized by geometry and photometry attributes, point cloud has been widely applied in the immersive services of various 3D objects and scenes. The development of even more precise capture devices and the increasing requirements for vivid rendering inevitably induce huge point capacity, thus making the point cloud compression a demanding issue. In this paper, we introduce several well-known compression algorithms in the research area as well as the boosting industry standardization works. Specifically, based on various applications of this 3D data, we summarize the static and dynamic point cloud compression, both including irregular geometry and photometry information that represent the spatial structure information and corresponding attributes, respectively. In the end, we conclude the point cloud compression as a promising topic and discuss trends for future works.