Parity non-conservation in nuclei is viewed as an inescapable consequence of weak interactions. This review, therefore, starts with the derivation of the effective weak Hamiltonian, which then acts as a perturbation mixing states of the opposite parity in nuclei. The connection between the effective weak Hamiltonian and various models of weak interactions (or quantum flavour dynamics, QFD) and the strong quantum chromodynamics (QCD) is briefly reviewed. The effective weak Hamiltonian serves as an input for determining the weak parity-violating potential. This weak potential is the main tool for connecting elementary particles with nuclear physics. Its derivation is discussed extensively, with special attention to one-boson-exchange (rho meson, pion, etc) contributions. Examples of theoretical and semi-empirical weak parity-violating potentials are given. Nuclear physics aspects of parity nonconservation in nuclei are also discussed. Calculations of the opposite-parity admixture to the particular nuclear state (once the weak potential is given as an input) depend on knowledge of the proper nuclear wavefunctions and on the inclusion of all corrections that are due to the residual interactions. Among those, short-range correlations (parts of the weak potential have a short range of -0.5 fm), pairing corrections and an effective charge factor are described. The gauge invariance of electromagnetic effects is discussed together with the parity-violating nucleonnucleon-photon vertex. Some important experimental data are tabulated and compared with theory. This is followed by a discussion of two-body problems, processes involving a-particles, photon decays of complex nuclei, parity non-conservation in nuclear scattering, and similar effects. This review also contains information on methods and difficulties encountered in experimental investigations. Where possible, general conclusions are drawn, tabulating logically permissible alternatives. This review tries to present an overall view of the present state of the investigation of parity non-conservation in nuclei. The list of references is not at all inclusive, but those which were selected usually contain hints for further reading.