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Bearingless permanent-magnet (PM) synchronous motors (BPMSMs) are a new type of machines combining the characteristics of conventional PM synchronous motors and magnetic bearings. With ever-increasing concerns on applications, such as high-speed electric machines, canned pumps, high-speed-precision mechanical processing, aeronautics and astronautics, flywheel energy storage, life science, vacuum technique, and semiconductor and biotechnology industries, there is a fast growing interest in BPMSMs. In this paper, after a general description of the generation principle of radial suspension forces, a comprehensive overview of BPMSMs is presented, with particular emphasis on mathematical models, motor topologies, and control strategies. Moreover, several possible development trends of the BPMSM are also discussed.