Over the recent years there has been an increased trend in the use of Reduced Order Models (ROM) for modeling the coupled aeroelastic system. Of all the ROM models,the Proper Orthogonal Decomposition Method (POD) has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the ease with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.