The high-speed electrical machines are widely used in different industries, such as machine tools, aerospace engineering, autonomous power engineering, etc. This chapter is devoted to the basics of high-speed electrical machines with high-coercitivity permanent magnets. It is considered in the application areas of high-speed electrical machines and their classifications. In addition, design problems of high-speed electrical machines are shown. To estimate the efficiency, loss calculations are performed. The obtained results can be used in the design of high-speed electrical machines with high-coercitivity permanent magnets and in their future development.