Traditional microwave transmission lines such as micro-strips cannot precisely manipulate electromagnetic modes, and hence traditional electronic information systems suffer from some bottlenecks such as spatial coupling, dynamic response, and performance robustness. To this end, metamaterials of spoof surface plasmon polaritons (SSPPs) provide a strategy to break these bottlenecks and have attracted many research interests in optical and information fields. To be specific, SSPP metamaterials can mimic the behaviors of optical surface plasmon polaritons and manipulate the electromagnetic fields at microwave and terahertz frequencies. Furthermore, with the configurational characteristics similar to those of planar circuits, the SSPP structures can be used to prepare the basic transmission lines of the next generation of integrated circuits. In addition, SSPPs can be divided into the propagation type and the localized type. The propagation type SSPPs, beginning with the three-dimensional structures, have been developed into the ultrathin corrugated metallic strip configurations. Based on the above configuration, scholars have established a new framework for microwave circuits and prepared typical passive and active SSPP devices including filters, antennas, amplifiers and frequency multipliers. Recently, an SSPP wireless communication system has been reported, which can achieve the non-line-of-sight wireless communications of sub-wavelength-spacing multichannel signals. Similarly, the spoof localized surface plasmon (SLSP) metamaterials have also developed from the three-dimensional structures to the ultrathin configurations, and have adopted spiral configuration, chain configuration, high-order mode, and hybridization mode to provide more degrees of freedom for the sub-wavelength scale control of electromagnetic waves. Finally, we systematically discussed the related theories and applications of SSPP metamaterials in the microwave circuits, including the basic concepts and configuration evolution of SSPP metamaterials, the passive and active SSPP devices, and the wireless communication system.