A deployable sunshield generally consists of layers flexible, wrinklefree multilayer membranes with high precision, deployable booms and its control equipments. The deployable booms can orderly unfold the multilayer membrane after on-orbit to realize its light control and heat control performance, and it can effectively improve the protection on the aerospace systems. The state-of-the-art of domestic and international deployable sunshield structures were classified and summarized according to their deployable methods of one dimensional axial, two-dimensional plane and three-dimensional circumferential way, as well as the comparison to different structural design and the membrane materials. Some key scientific problems for the sunshields were presented in stray light suppression, folding and deployable deformation mechanism, more field coupling on membranes under the extreme environment, low temperature thermal control, and other aspects of solar pressure moment and computing methods. In addition, some recommendations were also given for the sunshield progress and research in China.