Blue phases are known to appear in chiral liquid crystals in a small temperature range between the chiral nematic phase and the isotropic one. They are optically active, non-birefringent, and they show Bragg diffraction of light in the visible wavelength, measuring several hundred nanometers. Their exotic structures and properties result from the competition between chiral forces and packing topology. Recently, the blue phases have attracted the attention in the field of optoelectronics and photonics. The following article summarizes the basic properties, especially the frustration in the double twist molecular alignment which is the origin of stabilization of the blue phase, and history of the blue phase studies, and describes significant advances that have been recently reported.