A review is given of the principles and prospects of directed channeling of neutral particles and photons in perfect crystals and in crystals containing microchannels of arbitrarily small width. It is shown that, in all cases (including a homogeneous lattice), the channeling of x rays and $\gamma$ rays is accompanied by the modulation of the transverse structure of the wave and by a change in the longitudinal attenuation coefficient. The nontrivial special case of M\"ossbauer radiation channeling is investigated. A detailed discussion is given of the channeling of neutrons in crystals due to the ``optical'' Fermi interaction with lattice nuclei, and the magnetic dipole-dipole and coherent Schwinger interactions in magnetic and nonmagnetic crystals. The effects of spin waves, elastic waves, and domain walls on channeling are examined. A discussion is presented of the possibility of channeling of neutral atoms with internal electromagnetic resonances by the induced-dispersive ordering interaction that takes place when the resonance frequency is equal to a harmonic of the bounce frequency associated with longitudinal motion in the periodic lattice. Experiments on neutron and $\gamma$-ray channeling are analyzed.