Abstract: An overview is given of the present status of research on the blue phase of cholesteric liquid crystals. This blue phase has unusual properties with an order parameter exhibiting three－dimensional spatial periodicity, and is a stable phase state which appears in a narrow temperature interval (of the order of 0.1—1K). We describe briefly the properties of the BPⅠ, BPⅡ and BPⅢ phases ("fog state") which have been observed by many researchers. We introduce the main (phenomenological) theory of the blue phase—— the Ginzburg－Landau theory , and point out its practical physical significance.