The collective oscillations of charge density (plasmons) in conductive solids are basic excitations that determine the dynamic response of the system. In infinite two-dimensional (2D) electron systems, plasmons have gapless dispersion covering a broad spectral range from subterahertz to infrared, which is promising in light-matter applications. We discuss the state-of-the-art physics of 2D plasmons, especially in confined 2D electron systems in stripe and disk geometry, using the simplest approach for conductivity. When the metal gate is placed in the vicinity of the 2D electron system, an analytical description of the plasmon frequency and damping can be easily obtained. We also analyze gated plasmons in the disk when it was situated at various distances from the gate, and discuss in detail the nontrivial behavior of the damping. We predict that it is not a simple sum of the radiative and collisional dampings, but has a nonmonotonic dependence on the system parameters. For high-mobility 2D systems, this opens the way to achieve the maximal quality factor of plasma resonances. Lastly, we discuss the recently discovered near-gate 2D plasmons propagating along the laterally confined gate, even without applied bias voltage and having gapless dispersion when the gate has the form of a stripe, and discrete spectrum when the gate is in the form of disk. It allows for one to drive the frequency and spatial propagation of such plasmons.
Keywords: Drude model; confined magnetoplasmon; confinement of gated plasmon; near-gate plasmon; plasmon polaritons in confined two-dimensional electron systems; quantum well; two-dimensional plasmon.