This review is concerned with processes in which neutrinos are scattered (elastically or inelastically) by nucleons or electrons as a result of weak interactions involving neutral currents. The experimental data are summarized in detail and the restrictions which these data impose on the structure of the neutral currents are analyzed. Two particular gauge theories of the weak interaction are discussed, namely the well-known Weinberg-Salam model and the so-called vector model; both variants are in agreement with experiment for some appropriate value of the Weinberg angle or other analogous free parameter.