Optimum design of Controlled Diffusion Airfoils (CDA) is one of the main research fields in subsonic and transonic profile design of multistage compressor. In this paper, the importance of CDA studying, the originated background of CDA, the first generation CDA and the second generation CDA with the influence of cascade endwall flow are summarized. CDA is originated from the supercritical airfoil. Through controlling the diffusion on the suction surface of an airfoil, the shock wave can be eliminated or decreased, the loss reduced and the range of incidence increased. Around this criterion of airfoil design, many design methods are proposed, which can be classified into the inverse method and the direct method. In China, the beginning of the research for CDA is later than many other countries, and the studying is concentrated on the theory and design method.
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