Resonators of surface plasmons are discussed in this review. Any material supporting the excitation of surface plasmons, either by light, or by electron beams can be used for designing a resonator. Despite the number of materials supporting surface plasmons being restricted to a small number, noble metals, some two-dimensional materials as graphene, transition metal oxides, and several highly doped semiconductors have been used in plasmonic applications. Isolated and coupled metal nanoparticles, arrays of particles on substrates, nanoparticle suspensions, alternated metal and dielectric thin films, dielectric cavities in surfaces of noble metals and sheets and stripes of two-dimensional materials are typical examples of systems used for excitation of plasmonic resonances. These resonances have been used in a fast increasing number of applications: transformation of light beam properties, selective optical induced heating, sensing of chemical or biological compounds, enhancement of non-linear optical excitation in nanomaterials, optical coherence applications in quantum optics. The operating spectral range, variety of sizes, shapes and geometrical configurations that can be tailored and the exceptional optical properties of surface plasmons promote their use in a wide variety of applications at the nanoscale, where other types of resonators cannot be used, or are too inefficient.
We review a large variety of plasmonic resonators and their most relevant properties. We first discuss the fundamental properties of the plasmonic resonances, using simple physical models. Then we present a retrospective of applications evidencing the most relevant aspects of interaction of surface plasmons with matter and radiation. Finally we focus the most recent applications covering metamaterials, plasmonic materials with topological properties and resonators supporting plasmon-electron interaction.