Wear occurs at most solid surfaces that come in contact with other solid surfaces. While biological surfaces and tissues usually have the ability to repair minor wear damage, engineered self-healing materials only started to emerge recently. An example of a smart self-healing material is the material with imbedded microcapsules or microtubes, which rupture during crack propagation and release a healing agent that repairs the crack. Self-healing mechanisms are hierarchical in the sense that they involve interactions with different characteristic scale lengths. While traditional models of self-healing require equations with many degrees of freedom, taking into account the hierarchical organization allows us to reduce the number of equations to a few degrees of freedom. We discuss the conditions under which the self-healing occurs and provide a general theoretical framework and criteria for self-healing using the concept of multiscale organization of entropy and non-equilibrium thermodynamics. The example of a self-healed Al alloy reinforced with microtubes filled with Sn60Pb40 solder is discussed as a case study.