Airborne LiDAR point cloud filtering is a key step in point cloud processing. Lots of experts and scholars at home and abroad are doing research on point cloud filtering. In recent years, filtering is developed very fast and many other algorithms based on new theoretical background are proposed. Thus, it is urgent to summarize all kinds of filtering algorithms systematically. We classified all the algorithms into six categories based on the previous studies. The principles, implementation steps and existed problems of each class were also elaborated. This paper adopted the data sets provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) to compare the accuracy of each representative algorithm in each class and summarized their advantages and disadvantages. Last but not least, we provided some advices on how to further improve the accuracy and robustness of filtering algorithms. The review will be beneficial to point cloud data processing researchers to have more systematic, clear and accurate knowledge on filtering algorithms. It is also expected that this paper would make some contributions on extending filtering algorithms and improving point cloud post processing precision.