Two unstructured grid methods for unsteady flow simulation are presented, whose principles and algorithms in unsteady flow simulation are stressed. One is overset unstructured grid method, which has the advantages of unstructured grid and chimera grid and can handle problems with complex geometries and/or moving bodies. The wall distance of grid node is used as a parameter to classify the nodes and define the interpolation boundary of overset grid. A dynamic overset unstructured grid method is used to deal with the unsteady problems with multi-body moving. The other is dynamic unstructured grid based on Delaunay graph mapping, which can handle unsteady flow problems with body motion and deformation. In the method, a Delaunay graph is first generated using boundary nodes of computational grid and one to one mapping is built between Delaunay graph and the grid. The motion or deformation of body is realized by the moving of Delaunay graph and the new computational grid can be generated efficiently by the mapping. A number of cases(3D store separation, helicopter fuselage-rotor interaction, multi-airfoil with large trailing flap pitching, AGARD445.6 wing aeroelastic deformation)are used to validate the unstructured grid methods. All the results show that those methods are efficient in simulating unsteady problems.