Shape memory elastomers have revolutionised the world since their introduction in the 20th century. The ability to tailor chemical structures to produce a family of materials in wide-ranging forms with versatile properties has propelled them to be ubiquitous. Recent challenges in the end-of-life management of polymeric materials should prompt us to ask, ‘what innovations in polymeric materials can make a strong case for their use as efficient materials?’ The development of smart elastomers that can acquire, convey, or process a stimulus (such as temperature, pressure, electromagnetic field, moisture, and chemical signals) and reply by creating a useful effect, specifically a reversible change in shape, is one such innovation. Here, we present a brief overview of shape memory elastomers (SMEs) and thereafter a review of recent advances in their development. We discuss the complex processing of structure-property relations and how they differ for a range of stimuli-responsive SMEs, self-healing SMEs, thermoplastic SMEs, and antibacterial and antifouling SMEs. Following innovations in SEMs, the SMEs are forecast to have significant potential in biotechnology based on their tailorable physical properties that are suited to a range of different external stimuli.