The concept of self-healing synthetic materials emerged a couple of decades ago and continues to attract scientific community. Driven primarily by an opportunity to develop life-like materials on one hand, and sustainable technologies on the other, several successful approaches to repair mechanically damaged materials have been explored. This review examines chemical and physical processes occurring during self-healing of polymers as well as examines the role of interfaces in rigid nano-objects in multi-component composites. The complex nature of processes involved in self-healing demands understanding of multi-level molecular and macroscopic events. Two aspects of self-healing are particularly intriguing: physical flow (macro) of matter at or near a wound and chemical re-bonding (molecular) of cleaved bonds. These events usually occur concurrently, and depending upon interplay between kinetics and thermodynamics of the processes involved, these transient relations as well as efficiency are critical in designing self-healing materials. This review examines covalent bonding and supramolecular chemistry in the context of molecular heterogeneities in repair processes. Interfacial regions in nanocomposites also facilitate an opportunity for supramolecular assemblies or covalent bonding which, if designed properly, are capable of self-repairs.