It is well-established that interfaces play critical roles in biological and synthetic processes. Aside from significant practical applications, the most accessible and measurable quantity is interfacial tension, which represents a measure of the energy required to create or rejoin two surfaces. Owing to the fact that interfacial processes are critical in polymeric materials, this review outlines recent advances in dynamic interfacial processes involving physics and chemistry targeting self-healing. Entropic interfacial energies stored during damage participate in the recovery, and self-healing depends upon copolymer composition and monomer sequence, monomer molar ratios, molecular weight, and polymer dispersity. These properties ultimately impact chain flexibility, shape-memory recovery, and interfacial interactions. Self-healing is a localized process with global implications on mechanical and other properties. Selected examples driven by interfacial flow and shape memory effects are discussed in the context of covalent and supramolecular rebonding targeting self-healable materials development.