The field of stimuli-responsive, or smart polymers, has commanded significant interest over the past decade. However, most examples of stimuli-responsive polymers have relied on macroscopic changes that arise via simple alterations in chain conformation or changes in polymer-polymer or polymer-solvent interactions. In recent years, there has been an effort to expand the scope of modifiable variables to include the covalent architecture of a polymer through the use of reversible covalent bonds. Polymers capable of architectural transformation are those that can undergo changes in their chain topology (e.g., linear to branched, star to comb, etc.) via rearrangement in the chain structure. This approach has proven particularly interesting because it allows access to materials capable of dramatic macromolecular property changes that cannot be replicated by the more traditional approaches to responsive polymer systems, which often rely on solubility or swelling transitions in solution. This review aims to highlight the main synthetic strategies to architecture-transformable polymers, including dynamic-covalent and supramolecular chemistry approaches. In addition, the properties and applications of those smart polymers are highlighted. It is clear from recent research in this area that macromolecules capable of undergoing transformations in topology represent a paradigm shift in the field of stimuli-responsive materials.