The current state of the theory and experimentation in the field of interaction of relativistic electrons, positrons, and quanta of different energies with crystals in which the effect of channeling of particles plays an important role is reviewed. For relatively low energies, main attention is paid to effects of broadening of the spectral lines of emission in transitions between the levels of the transverse energy of the charged particles in the averaged field of the rows or planes of the crystal. The problem is studied on the basis of a theory that takes account of the deviation of the true potential of the crystal from the averaged potential of the rows or planes. In the region of medium energies ($\le$ 10 GeV) the main topic of the review is the stability of channeling, which reduces to the existence of integrals of motion in the averaged potentials. This problem is discussed in connection with the efficiency of conversion of the energy of the charged particles into energy of directional emission. In the region of high energies ($\ge$10 GeV), the review analyzes the various approaches in the theory of emission and formation of electron-positron pairs by photons in the field of the rows and planes of the crystal. A special place in the review is taken by a discussion of the possibility of channeling of quanta and neutrons in superlattices. Similarities and substantial differences are shown between this effect and the effect of channeling of charged particles of relatively low energies in crystals.