Shape memory polymer and its composites are a type of intelligent materials that can convert between the temporary shape and original shape under corresponding external stimuli. Shape memory polymer and its composites have many advantages， such as low density， low cost， large recoverable deformation and controllable stimulus mode， etc.， and have shown great application potential in the aerospace field， including space deployable structure， releasing mechanism， morphing aircraft， etc. Most of these applications are in the development stage， some of which has already completed the functional verification on the ground， and a few of which have been tested in space. This work first summarized the classification of SMP and SMPC， as well as the performance change of SMP under adverse spatial environment factors. Subsequently， space deployable structure of SMPC are summarized， including hinge， truss， solar array， SMPC releasing device， morphing structures and 4D printed deployable structures. Finally， the article looks forward to the development trend of materials and structures.