The justification for using the homogeneous-field approximation for the local description of the interaction of electrons (e$^-$), positrons (e$^+$), and high-energy $\gamma$-quanta with oriented crystals is discussed. Synchrotron-type dichroism and double refraction of $\gamma$-quanta, radiative self-polarization of e$^\pm$ and creation of transversely polarized e$^\pm$ in bent crystals are discussed. These phenomena can serve as the basis of methods of obtaining polarized beams of e$^\pm$ and $\gamma$ on the most powerful existing proton accelerators and those under construction. The review also discusses the effect of spin rotation of particles in bent crystals, which enables one to measure the magnetic moments of short-lived particles, and also to observe the fundamental quantum electrodynamical effect of variation of the anomalous magnetic moment of e$^\pm$ in an intense crystal field.