Shape memory polymers (SMP) can be deformed to a stable, temporary shape and recovered to their original shape by applying a stimulus. These networks rely on the presence of two types of net points to establish their permanent and temporary shapes. Classical strategies to stabilize temporary shapes rely on cooling below T-g/T-m where macromolecules become pinned in a stressed state. Recovery of the SMP usually involves heating to above the transition temperature where the permanent shape is remembered. Employing reversible binding groups (RBGs) in SMPs has emerged as an alternative strategy for stabilizing temporary shapes or imparting recyclability of the permanent shape. The use of dynamic chemistry often engenders additional functionality such as intrinsic self-healing characteristics or alternative shape recovery triggering strategies. SMPs bearing both supramolecular and covalent RBGs will be reviewed with an emphasis on hydrogen bonding, ionic interactions, metal-ligand coordination, and dynamic covalent exchange and addition reactions. (c) 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 1340-1364