In recent years, significant progress has been made in polymeric materials, which alter shape upon external stimuli, suggesting potential applications in robotics, biomedical engineering, and optical devices. These stimuli-responsive materials may be categorized into two classes: (i) shape-changing materials in which a specific type of shape-shifting is encoded in the original material structure and (ii) shape-memory materials, which do not possess any predetermined shape-shifting as prepared, yet allow programming of complex shape transformations on demand. While shape alterations in shape-changing materials are intrinsically reversible, shape memory is usually a one-way transformation from a metastable (programmed) to an equilibrium (original) state. Recently, different principles for both one-way reversible and two-way reversible shape memory have been developed. These offer a powerful combination of reversibility and programmability, which significantly expands the range of potential applications. The goal of this review is to highlight recent developments in reversible shape-shifting by introducing novel mechanisms, materials, and applications. (c) 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 1365-1380