With the development of optical communication and high power laser technology, magneto-optical isolators were studied and applied widely, which results in the development of magneto-optical crystals. A variety of new magneto-optical crystals were developed, and it is desirable to prepare large-size and high optical quality magneto-optical crystals. In this paper, the theory and application of Faraday magneto-optical effect is described breifly. Then the research progress on the crystals of rare-earth orthoferrite, rare-earth molybdate, terbium containing niobite, yttrium iron garnet, terbium containing garnet and several magneto-optical ceramics are reviewed. Finally, the future development of magneto-optical crystals is given.