The review examines the interaction of several charged particles in the final state of processes in the case when the reaction proceeds in two stages through an intermediate resonance. In an inelastic collision of arbitrary atomic particles X and Y a particle D is formed in a quasistationary state along with particle A: X + Y $\to$ A + D. As a result of the breakup D $\to$ B + C charged particles A, B, and C are formed in the final state. The Coulomb interaction of these particles (the post-collision interaction--PCI) exerts a strong influence on the cross section for the process. Reactions in which the effects of PCI are manifested are the excitation of atomic autoionized states by ions and electrons and the ionization of inner shells of atoms by collisions with ions, electrons or photons followed by Auger decay. Under the influence of PCI the spectra of the products of these reactions are distorted: the lines in the autoionization spectrum are broadened, shifted, and become asymmetric. A survey is given of the available theoretical concepts concerning PCI and of the accumulated experimental data providing evidence of its manifestation. The kinematic region in which the problem has a parametrically exact analytic solution is investigated thoroughly. Post-collision interaction in more complex processes in the final state of which four charged particles are involved is also examined. Experiments are discussed that make it possible to observe new manifestations of PCI. Various interference effects in PCI are examined.