Sophisticated polymeric materials with responsive properties, such as self-healing, are beginning to reach the market. Supramolecular polymers, i.e., polymers that owe their mechanical properties primarily to the reversible, non-covalent interactions, such as hydrogen bonding interactions, between the macromolecules, have frequently been employed as self-healing materials. The quadruple hydrogen bonding ureidopyrimidinone (UPy) unit is a particularly effective and versatile design motif, since it forms very strong but reversible linkages, and can be incorporated into virtually any type of polymer backbone, leading to materials with increased mechanical properties. Supramolecular polymers are presented, with an emphasis on those based on the UPy-unit, and their use in self-healing applications is highlighted and discussed.