This review describes the present status of research on the blue phase of cholesteric liquid crystals--a phase state of liquid crystals with unusual properties, whose order parameter exhibits three-dimensional spatial periodicity and which appears in a narrow temperature interval (of the order of 1$^\circ$). Experimental results and current theoretical models of the blue phase are presented. The phase transitions between the isotropic liquid, the blue phase, and the cholesteric phase are studied using Landau's theory. The discussion of methods for studying the blue phase emphasizes both the most informative optical methods and the theory of the optical properties of the blue phase. It is pointed out that the study of the blue phase is of substantial interest for the physics of the condensed state as a whole, and unsolved problems in this area are briefly discussed.