This review discusses the statistical properties of the scattering matrix in mesoscopic systems, focusing on two geometries: a quantum dot and a disordered wire. The quantum dot is a confined region with chaotic classical dynamics, connected to two electron reservoirs via point contacts. The disordered wire connects to reservoirs either directly or via point contacts or tunnel barriers. In the case of a superconducting reservoir, Andreev reflection occurs at the interface. The distribution of the scattering matrix for the quantum dot is described by Dyson's circular ensemble for ballistic point contacts or the Poisson kernel for point contacts with a tunnel barrier. For the disordered wire, the distribution is derived from the Dorokhov-Mello-Pereyra-Kumar equation, a one-dimensional scaling equation. The results are connected to the non-linear σ model, a supersymmetric field theory of localization. The distribution of scattering matrices is applied to various phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction. The review also discusses the statistical theory of energy levels, transmission eigenvalues, and correlation functions, and their implications for transport properties in mesoscopic systems. The review concludes with an overview of the field and directions for future research.This review discusses the statistical properties of the scattering matrix in mesoscopic systems, focusing on two geometries: a quantum dot and a disordered wire. The quantum dot is a confined region with chaotic classical dynamics, connected to two electron reservoirs via point contacts. The disordered wire connects to reservoirs either directly or via point contacts or tunnel barriers. In the case of a superconducting reservoir, Andreev reflection occurs at the interface. The distribution of the scattering matrix for the quantum dot is described by Dyson's circular ensemble for ballistic point contacts or the Poisson kernel for point contacts with a tunnel barrier. For the disordered wire, the distribution is derived from the Dorokhov-Mello-Pereyra-Kumar equation, a one-dimensional scaling equation. The results are connected to the non-linear σ model, a supersymmetric field theory of localization. The distribution of scattering matrices is applied to various phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction. The review also discusses the statistical theory of energy levels, transmission eigenvalues, and correlation functions, and their implications for transport properties in mesoscopic systems. The review concludes with an overview of the field and directions for future research.