Fifteen mechanochemical phenomena observed under compression and plastic shear of materials in a rotational diamond anvil cell (RDAC) are systematized. They are related to strain-induced structural changes (SCs) under high pressure, including phase transformations (PTs) and chemical reactions. A simple, three-scale continuum thermodynamic theory and closed-form solutions are developed which explain these phenomena. At the nanoscale, a model for strain-induced nucleation at the tip of a dislocation pile-up is suggested and studied. At the microscale, a simple strain-controlled kinetic equation for the strain-induced SCs is thermodynamically derived. A macroscale model for plastic flow and strain-induced SCs in RDAC is developed. These models explain why and how the superposition of plastic shear on high pressure leads to (a) a significant (by a factor of 3–5) reduction of the SC pressure, (b) reduction (up to zero) of pressure hysteresis, (c) the appearance of new phases, especially strong phases, which were not obtained without shear, (d) strain-controlled (rather than time-controlled) kinetics, or (e) the acceleration of kinetics without changes in the PT pressure. Also, an explanation was obtained as to why a nonreacting matrix with a yield stress higher (lower) than that for reagents significantly accelerates (slows down) the reactions. Some methods of characterization and controlling the SCs are suggested and the unique potential of plastic straining to produce high-strength metastable phases is predicted.