The miniaturization of electromagnetic devices is a long-term theme for the development of modern technologies to achieve higher flexibilities, better performances, and higher density integration. Surface plasmon polaritons (SPPs) provide a powerful solution for reducing the size of integrated electromagnetic device due to its deep subwavelength confinement. However, materials or structures that support SPPs inevitably have impurities or structural defects, which leads to the loss of the propagating mode. In order to avoid scattering from impurities or defects, topological structures are introduced to address issues of discontinuities and have been proved to be an effective solution. In this paper, we first review the recent efforts devoted to SPPs based optical devices and those of artificial surface plasmon in terahertz/microwave band, and then summarize several important topological systems of SPPs. Finally, we present our perspectives on the future developments of this field.