With the advancement of 3D sensing technologies, point clouds are gradually becoming the main type of data representation in applications such as autonomous driving, robotics, and augmented reality. Nevertheless, the irregularity inherent in point clouds presents numerous challenges for traditional deep learning frameworks. Graph neural networks (GNNs) have demonstrated their tremendous potential in processing graph-structured data and are widely applied in various domains including social media data analysis, molecular structure calculation, and computer vision. GNNs, with their capability to handle non-Euclidean data, offer a novel approach for addressing these challenges. Additionally, drawing inspiration from the achievements of transformers in natural language processing, graph transformers have propelled models towards global awareness, overcoming the limitations of local aggregation mechanisms inherent in early GNN architectures. This paper provides a comprehensive review of GNNs and graph-based methods in point cloud applications, adopting a task-oriented perspective to analyze this field. We categorize GNN methods for point clouds based on fundamental tasks, such as segmentation, classification, object detection, registration, and other related tasks. For each category, we summarize the existing mainstream methods, conduct a comprehensive analysis of their performance on various datasets, and discuss the development trends and future prospects of graph-based methods.