High torque density is a desirable feature of electrical machines used in traction applications, such as electric vehicle (EV)/hybrid electric vehicle (HEV) propulsion, wind turbines, more electric aircrafts, etc. The flux-modulated permanent magnet (FMPM) machine is considered as one of the most promising candidates to achieve high torque density. The incorporated gearing effect is ideal in reducing the rotating speed and amplifying the output torque of the FMPM machines. This paper aims at a comprehensive review of the topology evolution of the FMPM machines. Based on different structures, the FMPM machines are grouped into four categories: surface-type FMPM machines, spoke-type FMPM machines, partitioned stator FMPM machines, and bidirectional FMPM machines. The operating principles, advantages, drawbacks, and major applications of the FMPM machines are discussed in detail. In the end, the current state of the art, opportunities, challenges, and future trends of the FMPM machines are discussed. Therefore, this paper offers a systematic guidance on the selection and design of the FMPM machines.