Abstract: The processing, transmission, and semantic segmentation of point clouds are important analytical tasks in the field of 3D computer vision. Nowadays, the effectiveness of graph neural networks and graph structures in point cloud research has been confirmed, and graph-based point cloud (GPC) research continues to emerge. Therefore, a unified research perspective, framework and methodology need to be formed. This paper systematically sorts out various application scenarios of GPC research, including registration, denoising, compression, representation learning, classification, segmentation, detection and other tasks, summarizes the general framework of GPC research, and proposes a technical route covering the current GPC research. Specifically, this paper gives the hierarchical concept category of GPC research, including low-level data processing, intermediate representation learning, and high-level recognition tasks. GPC models or algorithms in various fields are reviewed, including static and dynamic point cloud processing algorithms, supervised and unsupervised representation learning models, and traditional or machine learning GPC recognition algorithms. The representative achievements and their core ideas are summarized, such as dynamically updating the nearest neighbor graph at each layer of feature space, hierarchical and parameter sharing dynamic point aggregation module, and segmentation accuracy improvement employing graph partitioning as well as graph convolution. The model performances are compared, including OA (Overall Accuracy), mAcc (Mean Accuracy) and mIoU (Mean Intersection over Union). Based on the analysis and comparison of existing models and methods, the main challenges faced by GPC are summarized, the corresponding research issues are put forward, and the future research directions are explored. The GPC research framework established in this paper is general and comprehensive, which provides field positioning, technical summary and macro perspective for subsequent researchers to engage in this new cross-field research of GPC. The emergence of point cloud research is the result of the rapid progress of detector hardware technology. The current situation of point cloud research is that the theoretical research lags behind the practice, and some key problems need to be solved. The development of point cloud research is not only a theoretical necessity, but also the application of half a century of waiting, will push artificial intelligence into a new era.