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Objectives: With the rapid development of the reality acquisition technologies, such as laser scanning and structured light scanning, point cloud has become a high-precision three-dimensional holographic representation for the physics world. As the third important data source, point cloud is very suitable for presenting 3D model and geographic and spatial information, and pushes forward an immense influence on smart city, autonomous driving application and augmented reality. However, the massive, unstructured, and uneven density of point cloud data brings challenges to onboard and offboard storage as well as real-time transmission. Hence, efficient compression methods, which balance between bit rate and quality, are mandatory for ensuring the storage and transmission of such data. Methods: Firstly, we describe different families of approaches in details and summarize the basic technologies that are usually used in 3D point cloud compression. Secondly, we provide detailed description of three open source point cloud codec algorithms and their coding performances. Finally, the promising development tendency of the static point cloud compression is summarized. Results: This paper summarizes the state-of-the-art of domestic and foreign static point cloud compression algorithms, the standard specifications released by moving picture experts group and evaluation metrics for point cloud compression. Conclusions: The purpose is to open up a vision for the further research on the static point cloud compression technology to a certain extent, boost the advancement of theoretical research significance and practical application value in this technical area. [ABSTRACT FROM AUTHOR]