Shape-memory polymers (SMPs) and their composite materials are stimuliresponsive materials that have the unique characteristics of lightweight, large deformation, variable stiffness, and biocompatibility. This paper reviews the research status of the mechanical models for SMPs, shape-memory nanocomposites and shape-memory polymer composites (SMPCs); it also introduces some spatially deployable structures, such as hinges, beams, and antennae based on SMPCs. In addition, the deformation types of 4D printing structures and the potential applications of this technology in robots and medical devices are also summarized.The mechanism of shape-memory cycles and the mechanical behavior of SMPs can be described by establishing thermomechanical models, which lay the theoretical foundations for the rational design of SMP structures. This section will focus on the constitutive models for SMPs, the micromechanical models of SMPNs, and the buckling behavior of SMPCs.