This review is devoted to polarization phenomena observed in the x-ray range. It is noted that x-ray polarization effects are due to two physical factors, namely, the diffraction of x-rays and the anisotropy of the x-ray susceptibility of atoms in crystals. Diffraction-induced birefringence, dichroism, and change in polarization state are very dependent on the degree of imperfection of the crystal. Effects associated with the anisotropy of x-ray susceptibility, which have not been adequately investigated so far, are discussed in some detail. The anisotropy can lead to a qualitatively new effect, namely, the appearance of additional reflections with unusual polarization properties that provide information about crystal structure and chemical bonding. Magnetic scattering of synchrotron x-rays has become a powerful tool for the investigation of magnetic ordering in crystals. Practical applications discussed in this review include different modern x-ray polarizers, analyzers, and quarter-wave plates for obtaining and analyzing circular polarizations.