This article reviews the current situation in the field of rare $K$ decays: the relevant phenomenology, the present experimental situation, and prospects for the near future. Study of rare $K$ decays can make a significant contribution in a number of different frontier areas of research in high-energy physics. In the area of $\mathrm{CP}$ violation, study of such rare decays as ${K}_{L}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{e}^{+}{e}^{\ensuremath{-}}$, ${K}_{L}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${K}_{L}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, and muon polarization in ${K}_{L}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ can provide important complementary information to what has been learned from the decay ${K}_{L}^{0}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$. Even though experiments with sufficient accuracy to make a meaningful study of $\mathrm{CP}$ violation are still a few years away, significant progress has been made in this general area during the last decade. A second major area of interest in the field of rare $K$ decays is the search for processes forbidden in the Standard Model, e.g., ${K}_{L}^{0}\ensuremath{\rightarrow}\ensuremath{\mu}e$ and ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}$. Various extensions of the Standard Model predict that these processes will occur with branching fractions in the range of ${10}^{\ensuremath{-}10}$ to ${10}^{\ensuremath{-}15}$. Experiments of the last decade have pushed the limits into the ${10}^{\ensuremath{-}10}$ to ${10}^{\ensuremath{-}11}$ range, and further improvements in sensitivity of one to two orders of magnitude can be expected in the next few years. $K$ decays allow one also to study higher-order weak-interaction processes such as ${K}_{L}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${K}_{L}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$, ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, which are forbidden to first order in the Standard Model. Because of strong suppression, these decay modes offer potential windows on new physics; in addition, they may offer the most reliable measurement of ${V}_{\mathrm{td}}$, one of the elements of the weak mixing matrix in the quark sector. The studies of the ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ channel have achieved data samples of close to 1000 events; the other two modes should be observed for the first time in the next few years. Finally, as a byproduct of these studies, one has been able to look simultaneously for new light particles into which the $K$ meson could decay. Limits obtained for various hypothetical particles are summarized.