Lattice instability due to plastic and elastic deformation under pressure induces many types of structure transformations, including changes of coordination number, cation ordering, electronic state such as charge disproportionation, charge transfer and electron density of state, and spin-lattice interaction. Nonhydrostaticity of compression brings metastable states or intermediate states, which are different from the thermo-dynamically stable phases, because they are temporary states in the dynamical process. Kinetic study of the pressure-induced transition is discussed in accordance with the in situ observation of time-resolved diffraction measurement. Besides the stress-strain relation, the crystallite size is an effective parameter of phase transition under pressure. Molecular dynamical calculation simulates the high-pressure phase transition.