Styrene butadiene styrene (SBS) block copolymers comprise of two phases structured domains involving polystyrene "hard" domains and butadiene "soft" domains.The styreneic domains provide a physical crosslink that enables SBS to behave like a highly flexible thermoplastic elastomer. Recently, with the rise of smart elastomers, SBS-based matrices are being extensively used in transforming them into elastomers that can exhibit shape change when excited with a range of stimuli (shape memory elastomers). With the advantages of long-range elasticity, reprocessability, and ability to be modified into various tailor-made shape morphing elastomers, the use SBSbased elastomers has exceptionally risen in the scope of deployable structures temperature sensors, snap fittings, and actuators. This review attempts to tether the recent development in SBS-based shape memory polymers along with highlighting the fabrication routes and the shape memory mechanistic pathway. The review introduces the concept of shape memory polymers, classification, and their characterization, followed by shape memory elastomers and finally one way/two-way SBS-based shape memory elastomers. In an attempt to blend both the scientific and the engineering realm, the narrative provides a concise overview of SBS-based shape morphing polymers' expanding boundaries.