In recent years, point cloud representation has become one of the research hotspots in the field of computer vision, and has been widely used in many fields, such as autonomous driving, virtual reality, robotics, etc. Although deep learning techniques have achieved great success in processing regular structured 2D grid image data, there are still great challenges in processing irregular, unstructured point cloud data. Point cloud classification is the basis of point cloud analysis, and many deep learning-based methods have been widely used in this task. Therefore, the purpose of this paper is to provide researchers in this field with the latest research progress and future trends. First, we introduce point cloud acquisition, characteristics, and challenges. Second, we review 3D data representations, storage formats, and commonly used datasets for point cloud classification. We then summarize deep learning-based methods for point cloud classification and complement recent research work. Next, we compare and analyze the performance of the main methods. Finally, we discuss some challenges and future directions for point cloud classification.