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With ever-increasing concerns on our environment, there is a fast growing interest in electric vehicles (EVs) and hybrid EVs (HEVs) from automakers, governments, and customers. As electric drives are the core of both EVs and HEVs, it is a pressing need for researchers to develop advanced electric-drive systems. In this paper, an overview of permanent-magnet (PM) brushless (BL) drives for EVs and HEVs is presented, with emphasis on machine topologies, drive operations, and control strategies. Then, three major research directions of the PM BL drive systems are elaborated, namely, the magnetic-geared outer-rotor PM BL drive system, the PM BL integrated starter-generator system, and the PM BL electric variable-transmission system.