The most important methods used in obtaining solutions to compressible flow around bodies at subsonic and supersonic velocities are reviewed. Both two- and three-dimensional flows are considered and important analytical methods are mentioned. Greater emphasis has been placed on numerical methods of solution and the main emphasis is places in electrical analogies to the equations of motion governing the flow. Use is made of the linearised “Hodograph” equations and electrical analogies are developed using the electrical potential tank, resistance networks and reactance networks. A new method, and an example, for the design of an aerofoil in compressible flow is given. Reactance networks are also proposed that enable the exact numerical solution for two-dimensional mixed subsonic and supersonic flow problems.