Surface plasmon polaritons (SPPs) are interactions between incident electromagnetic (EM) waves and free electrons on the metal-dielectric interface in the optical regime. To mimic SPPs in the microwave frequency, spoof SPPs (SSPPs) on ultrathin and flexible corrugated metallic strips were proposed and designed, which also inherit the advantages of lightweight, conformal, low profile, and easy integration with the traditional microwave circuits. In this paper, we review the recent development of SSPPs, including the basic concept, design principle, and applications along with the development from unwieldy waveguides to ultrathin transmission lines. The design schemes from passive and active devices to SSPP systems are presented respectively. For the passive SSPP devices, the related applications including filters, splitters, combiners, couplers, topological SSPPs, and radiations introduced. For the active SSPP devices, from the perspectives of transmission and radiation, we present a series of active SSPP devices with diversity and flexibility, including filtering, amplification, attenuation, nonlinearity, and leaky-wave radiations. Finally, several microwave systems based on SSPPs are reported, showing their unique advantages. The future directions and potential applications of the ultra-thin SSPP structures in the microwave and millimeter-wave regions are discussed.