This chapter proposes the conception of mobile nanodefects as a universal catalyst. It considers the different ways of realization by the mobile nanodefects (MNDs) of the catalytic activity in various physical and chemical processes in solids. MNDs with an excess of free volume demonstrate the catalytic activity when they approach orientationally immobile chemically inert classic active centers in solids. With the help of the catalytic activity of MND, the nontrivial features of the industrial important energy-saving high-temperature process of polymers shear grinding are explained. The type of catalysis by MND was proposed for an explanation of non-trivial features of grinding of polymers; when such polymers expose to intense shear stresses. Such grinding was seen as the result of action on the polymers simultaneously two connected chemical stage of MND (mobile vacancies and cracks of super-critical size). One fundamental problem of chemical physics is the study of the mechanism of solid-phase redox reactions with electron transfer on the abnormally large distance.