Trans-1,4-polyisoprene (a thermoplastic crystalline polymer) and polystyrene (an amorphous or semicrystalline polymer) have been frequently used as important matrix materials for the formation of nanocomposites. Trans-1,4-polyisoprene has crystallinity and toughness properties, whereas polystyrene has transparent and brittle nature. These matrices have revealed shape memory effects through the inclusion of carbon nanoparticles like graphene and carbon nanotube, as well as inorganic nanoparticles like titania, silica, and metal nanoparticles. The nanoparticle addition has been found to induce shape changes as well as microstructural and physical property alterations in the matrices. This state-of-the art review article reports on the stimuli responsiveness of important categories of trans-1,4-polyisoprene and polystyrene based nanocomposites. These nanomaterials revealed important thermal, electric, and radiation induced responses. High performance shape memory effects have been observed depending upon the nanoparticle type, contents, and interactions with the polymer network. With the carbon nanoparticles like carbon nanotube, graphene, or carbon black, trans-1,4-polyisoprene revealed high shape recovery responses of 95%–99%. The nanocomposites of copolymers or blends of trans-1,4-polyisoprene also depicted the shape recovery of up to 100%. The shape memory nanocomposites of polystyrene and its blends and copolymers with different types of nanoparticles exhibited effective thermo responsive and electro active shape memory behavior. Consequently, the effective shape memory effects have been attributed to the homogeneous nanoparticle dispersion as well as the network formation for an active polymer chain switching.