Abstract: The development of compressor aerodynamics is reviewed. The significance of studying the fine structure of flow field is emphasized. The roles of experimental investigation and numerical analysis in improving the understanding of this structure and the related problems are discussed.Transonic flow, viscous flow and unsteady flow are surveyed as three main fields in further development of the compressor aerodynamics. The topics in these fields are elaborated so that the difficulties in research on them are revealed and some suggestions are proposed. In the meantime, the emphasis is placed on the problems particular to the compressor aerodynamics,