In the field of hypersonic flight technology, especially the study of high-enthalpy flows, the hypersonic wind tunnel test, at present, is still the most reliable and convenient research method. For the development of hypersonic wind tunnels, one of the most important performance indicators is the uniform flow quality, which depends on the theories and methods of hypersonic nozzle design, and is the core technique of wind tunnel design. For the design of a two-dimensional axisymmetric contour nozzle, this paper first reviews the main theories and traditional design methods that have played an important role in the design of hypersonic nozzles, including the theoretical methods, the approximate methods, and the correction methods for both. Then, due to the high-temperature gas effects, the difficulties and problems faced in the design of high-enthalpy nozzles are analyzed in detail. In terms of the changes in the physical properties of the test gases, the development of high-temperature boundary-layer, and the effects of non-equilibrium processes, this paper also reviews the domestic and foreign research progresses in the design of hypersonic and high-enthalpy nozzles. Finally, the development of theory and method for designing the high-enthalpy nozzle is prospected, and we expect it to promote the development of hypersonic nozzle design technology in China.