Abstract: The optical telescopes for space-based gravitational wave missions play an important role in the measurement, which both expand the beam going to the far spacecraft and efficiently collect the beam sent from the far spacecraft. The telescope, as part of the interferometric path, directly affects the measurement noise. Compared with the imaging system, the telescope for space gravitational wave observatory not only has high requirements on wavefront quality, but also has extremely high requirements on stray light performance and optical path stability, and the latter two are more challenging. The research progress of the telescope's optical system, optical-mechanical structure, space environment and thermal design, stray light simulation and suppression, and stability measurement is reviewed, which can provide a reference for the development of space gravitational telescope in our country.