Numerous experiments have documented that combination of severe plastic deformation and high mean pressure during high-pressure torsion in rotational metallic, ceramic, or diamond anvils produces various important mechanochemical effects. We will focus here on four of these: plastic deformation (a) significantly reduces pressure for initiation and completion of phase transformations (PTs), (b) leads to discovery of hidden metastable phases and compounds, (c) reduces PT pressure hysteresis, and (d) substitutes a reversible PT with irreversible PT. The goal of this review is to summarize our current understanding of the underlying phenomena based on multiscale atomistic and continuum theories and computational modeling. Recent atomistic simulations provide conditions for initiation of PTs in a defect-free lattice as a function of the general stress tensor. These conditions (a) allow one to determine stress states that significantly decrease the transformation pressure and (b) determine whether the given phase can, in principle, be preserved at ambient pressure. Nanoscale mechanisms of phase nucleation at plastic-strain-induced defects are studied analytically and by utilizing advanced phase field theory and simulations. It is demonstrated that the concentration of all components of the stress tensor near the tip of the dislocation pileup may decrease nucleation pressure by a factor of ten or more. These results are incorporated into the microscale analytical kinetic equation for strain-induced PTs. The kinetic equation is part of a macroscale geometrically-nonlinear model for combined plastic flow and PT. This model is used for finite-element simulations of plastic deformations and PT in a sample under torsion in a rotational anvil device. Numerous experimentally-observed phenomena are reproduced, and new effects are predicted and then confirmed experimentally. Combination of the results on all four scales suggests novel synthetic routes for new or known high-pressure phases (HPPs), experimental characterization of strain-induced PTs under high-pressure during torsion under elevated pressure.