With the wide applications of three-dimensional (3D) meshes in digital entertainment, television animation, virtual reality, and other fields, there are more and more processing techniques for 3D meshes, including compression, simplification, watermarking, and denoising. These processing techniques will inevitably lead to various distortions in 3D meshes. Therefore, how to preferably evaluate the visual quality of 3D meshes becomes an urgent problem to be solved at present. This paper reviews the objective quality assessment methods for 3D meshes developed during the past 20 years. First, some technical indexes for 3D mesh quality assessment and several public databases are introduced. Second, the quality assessment methods for existing typical three-dimensional meshes are classified, and their respective characteristics are introduced. Then, the typical algorithms introduced in the commonly used databases are tested and compared. Finally, the objective quality assessment methods of 3D meshes are summarized and prospected.