Shape-memory polymers (SMPs) and their composites (SMPCs), as a kind of smart materials, can respond to particular external stimulus and recover the original shape. They present outstanding features encompassing shape-memory effect, deformability, biocompatibility, variable stiffness, lightweight, and so on. They have attracted considerable research interest in recent years. Several stimulation methods to actuate the deformation of SMPs and SMPCs, of which the thermal stimulation is the common one, and many types of reinforcements have been developed over the past few years. It is revealed that the SMPC thermal and mechanical properties can be improved by introducing a number of reinforcements. Therefore, to well investigate the SMPC characteristics upon exposure to a specific external stimulus, a deep knowledge and understanding of the potential reinforcements as well as the available stimulation methods are crucial. In this review, reinforcements such as fibers, ceramics, and nanocarbons are first concisely presented. Next, numerous novel stimulation methods used to trigger the memory effect of the SMPCs are introduced, where the mechanisms of electrical, magnetic, thermal, light, and solution stimulations are briefly discussed. Finally, considering the increase of the number of interesting reinforcements as well as the efficient stimulation methods, SMPCs are expected to have great potential applications in different fields.