Smart materials are much discussed in the current research scenario. The shape memory effect is one of the most fascinating occurrences in smart materials, both in terms of the phenomenon and its applications. Many metal alloys and polymers exhibit the shape memory effect (SME). Shape memory properties of elastomers, such as rubbers, polyurethanes, and other elastomers, are discussed in depth in this paper. The theory, factors impacting, and key uses of SME elastomers are all covered in this article. SME has been observed in a variety of elastomers and composites. Shape fixity and recovery rate are normally analysed through thermomechanical cycle studies to understand the effectiveness of SMEs. Polymer properties such as chain length, and the inclusion of fillers, such as clays, nanoparticles, and second phase polymers, will have a direct influence on the shape memory effect. The article discusses these aspects in a simple and concise manner.