High performance inlet diffusers for efficient operation in supersonic and hypersonic Mach number ranges can be designed with existing techniques. Design philosophy, however, is complicated. For optimum propulsion system performance, minimum external drag must be consistent with maximum internal pressure recovery. Best inlet performance, however, is restricted by compression limit, viscous and real gas effects, and considerations of off-design performance. Minimum weight, complexity, and cooling requirements are also essential, although the latter may be incompatible with optimum inlet performance. The most desirable mechanical-structural features are embodied by the fixed geometry inlet type, whereas optimum performance potential is demonstrated by the variable geometry type. Both inlet types have a place in the mission spectrum that can be envisioned for air-breathing propulsion systems.