The compressor performance map with variable speed is described. A relatively simple 1D method for map prediction for a single stage based on the compressor duty is described. This provides good estimates of the expected performance map of a well-designed stage with only limited information about the geometry and gives a useful guide as to the performance map that can typically be achieved. The extension of the typical compressor performance map, with positive flow, positive rotation and positive pressure rise, into four regions with negative flow, negative pressure rise and reverse rotation, is described. The prediction of the performance of multistage compressors is described based on the principle of stage-stacking calculations. Matching of an impeller with a vaned diffuser at different tip-speed Mach numbers is considered. The matching of a compressor with a turbine in a micro gas turbine is described. The matching of a centrifugal compressor with a radial inflow turbine in a turbocharger is examined and demonstrates the advantages of the use of a turbine bypass valve or a turbine with variable inlet guide vanes to improve the performance.