Abstract: The flux-modulation linear permanent magnet machines (FMLPMMs) naturally have higher thrust density and lower thrust force ripple due to the use of flux-modulation principle (also known as magnetic gear effect). Therefore, they have become one of the research hotspots in the field of linear motors in recent years. The main purpose of this paper is to systematically review the research work on the topological structure of FMLPMMs. Firstly, this paper introduced the evolution of the topological structure of the FMLPMMs, classified and summarized the existing topological structures. Secondly, since thrust density and thrust force ripple were the two most important performance parameters of linear machines, this paper introduced in detail how to further improve the thrust density and suppress the thrust force ripple of FMLPMMs. Finally, the future development direction and application prospect of FMLPMMs were discussed in this paper.