Shape memory polymers (SMPs) are polymeric smart materials, a class of stimuli‐responsive polymers that can return to their initial shape from a programmed temporary shape under the application of external stimuli, such as light, heat, magnetism, and electricity. Because of these unique features, SMPs can find applications in many fields, like aerospace, biomedical devices, flexible electronics, soft robotics, shape memory arrays, and 4D printing. The comparatively low density, low cost, easy biodegradability, and biocompatibility make SMPs a better candidate for shape memory applications. Among them, thermo‐responsive SMPs can revert to their permanent shape depending on a temperature greater than their polymer transition temperature. Thermo‐responsive SMPs combine semi‐crystalline or elastomeric polymers with improved mechanical and electrical properties. Integrating nanofillers into the polymer elastomer matrices can further enhance these properties, forming shape‐memory polymer nanocomposites (SMPNCs). This review focuses on the basics, design, and classifications of thermo‐responsive SMPs and the characteristics of elastomers and blends of polymers used. Incorporating various nanofillers to get SMPNCs to have improved properties over SMPs is also presented. The importance of Tg (glass transition temperature) and Tm (melting temperature) based SMPs and SMPNCs, various elastomers used, and the methods for preparation like solution casting, melt compounding, in situ polymerization, and their possible future applications are also discussed.