Synthetic self-assembled systems combine responsiveness and reversibility with the ability to perform chemical tasks such as molecular recognition and catalysis. An unmet challenge is the construction of polymeric materials that, like nature's tubulin, are simultaneously reversible and capable of useful physical tasks. We report here a class of reversibly formed polymers that show covalent-polymer mechanical integrity in solution and in the solid state. Non-Newtonian, polymeric behavior is observed despite the low molecular weight of the individual subunits and the seemingly weak forces holding the assemblies together. These polymers assemble through self-complementary hydrogen bonding and by physical encapsulation of small molecules; accordingly, the emergent macroscopic structure and function can be controlled by appropriate chemical signals.