Rapid development of wearable electronic devices stimulates the demand for matched energy storage devices. Such a complex application requires electronic devices and their power units to possess mechanically deformable ability and even healing capability to accommodate large scale mechanical deformation and self-heal cracks or fractures. Supercapacitors (SCs) are regarded as promising power units for wearable electronic devices due to the advantages of high power density, rapid charge rate, ultra-long life, great stability and safety. But conventional rigid SCs or primarily flexible SCs (bendable or twistable) are far from the requirements of practical applications of wearable electronic devices. SMART SCs with intensively deformable or healable abilities have been developed to satisfy these rigorous demands and have become a hot topic recently. In this article, we introduce the recent progress in this booming research area of compressible, self-healable, and shape memory SCs. For each type of these SMART SCs, the device or electrode structure design, the functional materials and their working mechanism, and the employed electrolyte are discussed in detail. Moreover, we also outline the challenges and perspective for the development of advanced SMART SCs. Both the mechanical and electrochemical performance of the SMART SCs require improvement. Meanwhile, it will be a fascinating trend to integrate multiple mechanical and non-mechanical functions into SMART SCs to make them novel self-powered multi-functional units in the near future.