Surface plasmon polaritons (SPP) arising from the interactions between electrons and photons at the metal/semiconductor-dielectric interfaces, and spoof surface plasmons (SSP) supporting by the metamaterials or the interactions between surface electrons and terahertz/microwave waves of polyatomic crystals, are the essential foundation for breaking the diffraction limit and building integrated terahertz active/passive devices. This paper introduces the basic principles, evolution processes of conventional optical SSP, terahertz SPP and graphene surface plasmon polaritons (GSP). The detailed summary and discussion of terahertz plasmons in the applications of terahertz sources, passive devices, super-resolution imaging and so on are also presented. In the last, we discuss the developing prospects of the terahertz plasmons.