This review is concerned with physical phenomena which have not as yet been observed, namely, effects associated with the nonconservation of parity in atomic transitions. The observation of some of these effects at the current level of optical research appears to be within the range of realistic expectations. Experiments of this kind should throw light on the weak interaction between electrons (or muons) and nucleons, due to the so-called neutral currents, which has not as yet been observed. The general form of this interaction, which does not conserve parity but is CP-invariant, is suggested. Effects associated with the nonconservation of parity in hydrogen and hydrogen-like atoms, heavy atoms, and $\mu$-mesic atoms are considered. Possible experiments designed to verify the existence of these effects are discussed (measurement of the circular polarization of radiation emitted by unpolarized atoms, rotation of the plane of polarization in optically inactive media, and so on).