Abstract: CFD methods forunsteady flow simulations are reviewed in this paper, includingmoving grid generation techniques and unsteady numerical methods.Based on the topology of computational grids, two types ofunsteady numerical methods are discussed, e.g. the methods basedon structured grids and unstructured/hybrid grids, respectively.Their advantages and drawbacks are analyzed with regard toefficiency, robustness for complex geometries and other features.In the framework of structured grids, several moving gridtechniques are reviewed, including the rigid moving structuredgrid approach, the deforming structured grid technique withtrans-finite interpolation, overlapping moving structured gridtechnique, and patched moving structured grid technique. Then someunsteady numerical methods on structured grids are discussed inthe systems of inertial and non-inertial coordinates. In addition,the discretization schemes in temporal direction and the GeometricConservation Law (GCL) are emphasized for unsteady simulations onmoving grids. In the context of unstructured/hybrid grids,overlapping unstructured grid technique, re-meshing unstructuredgrid technique, node-relaxation approach based on `Spring analogy'and Delaunay mapping are reviewed and compared. And, a combineddynamic unstructured/hybrid grid method developed by the authorsis suggested, which is a kind of coupled method of `Spring'relaxation, Delaunay mapping and local re-meshing. The GCLapproach, the convergence acceleration methods, and numericalschemes for unsteady incompressible flows are discussed forunsteady flow solvers on unstructured/hybrid grids. Some examplesand applications performed by the authors are given at the end ofthe paper.