The unstructured mesh deformation in dynamic meshes is one of the key techniques in computational fluid dynamics and solid mechanics. This paper presents recent advances in the researches on unstructured mesh deformation, and makes a detailed classification of mesh deformation approaches. The existing mesh deformation methods are classified into pseudo-structural approach, partial differential equation and algebraic method. The advances and properties of main approaches of mesh deformation are summarized. The main research fields including mesh deformation, dynamic mesh generation with complex boundary under irregular deformations, dynamic mesh generation in 3D, parallel dynamic mesh generation and moving grids technique, are discussed in details. The trends of mesh deformation investigations are briefly presented as well.