Abstract: CFD technique can be used to study aeroelasticproblems with aerodynamic non-linearity. The disadvantage of the CFD basedaeroelastic direct simulation is the high computational cost which preventsit to be used for qualitative analysis or parametric design. CFD based ROM(reduced order model) technique can solve the contradictionbetween computational efficiency and computational quality, and thecontradiction between complexity and convenience for analysis and design. Areview on two kinds of ROM and harmonic balance for nonlinearunsteady aerodynamics is made in this paper. Recent aeroelastic researches based onthese methods are summarized. The advantages of these methods arecompared and the future development is discussed.