During the past decade, the Lewis Laboratory of the NACA was engaged in intensive research on the aerodynamics of high-performance axial-flow compressors. The focal point of this program, the development of the transonic compressor, is briefly reviewed, and the basic significance of the results is discussed. Following this, a re´sume´ of succeeding experimental single and multistage investigations and analytical studies is given to indicate the scope of the work and the major results achieved. An extensive bibliography covering the research effort during this time is included.