Classifications of different types of turbomachines are reviewed to define precisely what is meant by a radial flow turbocompressor. Single-stage compressors and different configurations of multistage compressors are introduced. The basic operating principle of turbocompressors, the Euler turbine equation, is valid for all turbomachines. Numerous applications of radial flow turbocompressors are described, including gas turbines for power generation and propulsion, turbochargers, oil and gas processing, wastewater treatment and the compression of industrial gases in refrigeration and industrial processes. Newer applications in fuel cells and in microcompressors are introduced. This gives an overview of the large range of duty in terms of volume flow rate and pressure ratio for which these machines are used. Some of the special aerodynamic features that are relevant to their design in different applications are highlighted. Aspects of the history of compressors are also given together with a short overview of other books, technical journals and conferences on this topic.