Shape memory and self-healing polymer nanocomposites have attracted considerable attention due to their modifiable properties and promising applications. The incorporation of nanomaterials (polypyrrole, carboxyl methyl cellulose, carbon nanotubes, titania nanotubes, graphene, graphene oxide, mesoporous silica) into these polymers has significantly enhanced their performance, opening up new avenues for diverse applications. The self-healing capability in polymer nanocomposites depends on several factors, including heat, quadruple hydrogen bonding, π–π stacking, Diels–Alder reactions, and metal–ligand coordination, which collectively govern the interactions within the composite materials. Among possible interactions, only quadruple hydrogen bonding between composite constituents has been shown to be effective in facilitating self-healing at approximately room temperature. Conversely, thermo-responsive self-healing and shape memory polymer nanocomposites require elevated temperatures to initiate the healing and recovery processes. Thermo-responsive (TRSMPs), light-actuated, magnetically actuated, and Electrically actuated Shape Memory Polymer Nanocomposite are discussed. This paper provides a comprehensive overview of the different types of interactions involved in SMP and SHP nanocomposites and examines their behavior at both room temperature and elevated temperature conditions, along with their biomedical applications. Among many applications of SMPs, special attention has been given to biomedical (drug delivery, orthodontics, tissue engineering, orthopedics, endovascular surgery), aerospace (hinges, space deployable structures, morphing aircrafts), textile (breathable fabrics, reinforced fabrics, self-healing electromagnetic interference shielding fabrics), sensor, electrical (triboelectric nanogenerators, information energy storage devices), electronic, paint and self-healing coating, and construction material (polymer cement composites) applications.