A review is presented of the theory of optical properties of cholesteric liquid crystals (CLC). The diffraction nature of the unusual optical properties of CLC is exhibited in the simplest and most easily visualizable kinematic approximation of diffraction theory. A quantitative description of the optical properties is given based on the exact solution of Maxwell equations for light propagated along the optical axis of CLC and within the framework of the dynamic diffraction theory for an arbitrary direction of propagation. Considerable attention is devoted to the manifestation of the connection between the structural and optical properties of the CLC observed when light is propagated at an angle to the optical axis of the CLC and when the CLC structure is distorted by an external field. Investigations of the optical properties of absorbing CLC reveal that suppression of light absorption in the selective reflection band is analogous in its nature to the well-known Borrmann effect in x-ray diffraction. Different approaches to the optics of imperfect CLC which frequently most nearly correspond to the conditions of actual experiments are described. A theory of the optical properties of chiral smectic crystals is presented. This theory, on the whole, is analogous to that for CLC, but it predicts a number of qualitative differences in the optics of chiral smectic crystals. The theory and special features of the Vavilov-Cherenkov radiation in CLC is briefly presented. A comparison is made of the theoretical results with the experimental data and the most promising directions for theoretical and experimental research are indicated.