This review by C. W. J. Beenakker discusses the statistical properties of the scattering matrix in mesoscopic systems, focusing on two geometries: quantum dots and disordered wires. Quantum dots are confined regions with chaotic classical dynamics coupled to electron reservoirs, while disordered wires connect to reservoirs either directly or via point contacts or tunnel barriers. The distribution of the scattering matrix in quantum dots follows Dyson's circular ensemble for ballistic point contacts or the Poisson kernel for tunnel barriers. For disordered wires, the distribution is derived from the Dorokhov-Mello-Pereyra-Kumar equation, a one-dimensional scaling equation. The review also explores the equivalence of this distribution to the non-linear $\sigma$ model, a supersymmetric field theory of localization. The distribution of scattering matrices is applied to various physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in Josephson junctions. The article concludes with a discussion of future research directions, particularly the extension of random-matrix theory to thin-film and bulk geometries.This review by C. W. J. Beenakker discusses the statistical properties of the scattering matrix in mesoscopic systems, focusing on two geometries: quantum dots and disordered wires. Quantum dots are confined regions with chaotic classical dynamics coupled to electron reservoirs, while disordered wires connect to reservoirs either directly or via point contacts or tunnel barriers. The distribution of the scattering matrix in quantum dots follows Dyson's circular ensemble for ballistic point contacts or the Poisson kernel for tunnel barriers. For disordered wires, the distribution is derived from the Dorokhov-Mello-Pereyra-Kumar equation, a one-dimensional scaling equation. The review also explores the equivalence of this distribution to the non-linear $\sigma$ model, a supersymmetric field theory of localization. The distribution of scattering matrices is applied to various physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in Josephson junctions. The article concludes with a discussion of future research directions, particularly the extension of random-matrix theory to thin-film and bulk geometries.