The three-mirror reflective optical system can achieve high optical performance because of its ability to correct the aberrations of spherical aberration, coma and astigmatism at the same time. Based on the characteristics of small number of mirrors and acceptable alignment complexity, it is widely used in the field of optical imaging. In particular, the off-axis three-mirror optical system occupies an important position in high-performance optical instruments and equipment due to its many advantages, such as with unobscuration and with ability of large field of view. Taking the development of typical three-mirror optical system as the main line, various types of three-mirror optical systems were introduced comprehensively, including coaxial three-mirror optical system, two-axis three-mirror optical system, off-axis three-mirror optical system and afocal three-mirror optical system, their optical configuration characteristics, relevance and optical system performance were discussed, and design examples were gived for researchers in the field of optical design.