Abstract: The finite element mesh is the key link between the geometry model and the numerical simulation, and its automatic adaptive generation is still a key problem to be studied. In this paper, the research of triangular surface meshes, tetrahedral meshes, quadrilateral surface meshes and hexahedral meshes is reviewed. This paper summarizes the methods of unstructured mesh generation, and introduces the mainstream methods and engineering techniques of triangular mesh and tetrahedral mesh generation in detail. Furthermore, the technology and development of structured mesh generation are analyzed, and the principles, advantages and disadvantages of various generation methods of quadrilateral and hexahedral meshes are discussed.