Mesh deformation is a main method to implement the computational mesh deformation with a moving boundary in computational aeroelasticity. First, an investigation of the status of the current advances in the researches on mesh deformation is presented in this paper, and some common mesh deformation approaches in recent years are reviewed in detail, which are spring analogy method, elastic solid method, transfinite interpolation method, Delaunay graph method, radial basis function method and temperature analogy method. Besides, based on the established models, the existing methods can be classified into physical model method, mathematical interpolation method and hybrid approach. A brief introduction of each method is made on theoretical method and research advance. The main emphasis is on the difference among the three methods of advantages and disadvantages as well as properties including deformation capability, deformation quality and efficiency. As an important aspect in computational aeroelasticity, the calculation data transformation between flow field boundary and structure boundary is summarized as well. At last, the present problems of mesh deformation which are frequently encountered in computational aeroelasticity are discussed, and in order to meet the needs of projects, possible prospects in future mesh deformation investigations are also proposed.