In recent years, a wide range of novel smart soft active materials have been developed, and the applications of soft active materials now have covered various important fields including aerospace, automobile, telecommunications, and so forth. This talk mainly focuses on recent progresses on Soft Active Polymers such as Shape Memory Polymer (SMP), Electro-Active Polymer (EAP) and their nanocomposites, as well as the applications Firstly, the recent advances in synthesis of novel epoxy-based SMP, styrene-based SMP, cyanate ester-based SMP, polyurethane-based SMP, design and characterization of SMP composites (SMPCs) filled with nickel chains, short carbon fiber, carbon nanotube chains, carbon nanopaper, and so on, are summarized in this work. The SMP driven approaches, including heat, electricity, light, magnetic field, microwave, water and solvent have been introduced. In addition, a detailed overview of the recent progresses of SMPCs used in the space deployable structures (i.e. SMPC hinge, truss and frame) was proposed in this research. The fabrication of morphing structures and smart mandrels using shape memory polymers was also studied. For the sake of reducing the dynamic vibration structure, some adaptive structures such as macro fiber composite (MFC) actuators were introduced. Then several multifunctional nanocomposites such as electrospun nafion nanofibers, self-heating fiber reinforced polymer composite were proposed, as well as their applications. Finally, the mechanical behaviors of shape memory polymer and its composite such as post bucking behaviors of SMPC and mechanism of multi-shape memory effect of SMP were also researched for their better applications.