Abstract: The optimum design of Controlled Diffusion Airfoils (CDA) is one of the main research fields in subsonic and transonic profile design for multistage compressor.This paper reviews the necessity of CDA research,the background of CDA development,the features and design methods of first generation CDA and the second generation CDA with consideration of cascade endwall flow.The CDA is originated from the supercritical airfoil.Controlling the diffusion on the suction surface of an airfoil,can eliminate or decrease the shock wave,reduce the loss and enlarge the range of incidence.Around this criterion of airfoil design,many design methods have been proposed,which can be classified into inverse method and direct method.The CDA research in China started later than many other countries,and concentrated mainly on its principles and design methods.