—Metamaterials offer great promise for engineering electromagnetic properties beyond the limits of natural materials. A typical example is the so-called spoof surface plasmons (SPs), which mimic features of optical SPs without penetrating metal at lower frequencies. Spoof SPs inherit most of the properties of natural SPs, including dispersion characteristics, field confinement, localized resonance, and subwavelength resolution, and therefore are highly expected to offer a new solution for low-frequency applications. With the development of spoof SPs, three different theories have been introduced. The first one is the description of subwavelength corrugated metal surfaces by a metamaterial that hosts an effective plasma frequency. The second one is developed with high-index contrast grating, which can realize propagation with ultra low loss and localization with ultrahigh Q-factor resonance. The last one is structural dispersion induced SPs, a perfect low-frequency analogue of optical SPs, realized by exploiting the well-known structural dispersion waveguide modes only with positive-ε materials. Here, the developments of these three theories including propagation and localized SPs are reviewed, focusing primarily on the fundamental and representative applications. © 2022, Electromagnetics Academy. All rights reserved.