A number of experimental methods have been applied to study the kinetics of high-pressure solid-state amorphization for some covalent crystals (Si, Ge and GaSb), molecular crystals, C60 and ionic oxides (stishovite and H2O), as well as the amorphous-to-amorphous transitions for H2O and GeO2. The low activation energy for the stishovite → a-SiO2 transition and appreciable variation of kinetic characteristics in the covalent compounds, depending on the number of components, were observed. Using high-pressure solid-state amorphization it is possible to obtain amorphous tetrahedral carbon by compression of C60-crystals. We have shown that the P-T kinetic lines for amorphization smoothly convert to the ordinary crystal-to-crystal hysteresis lines at high temperatures. For the first time experimental evidence for elastic softening in the vicinity of crystal-to-amorphous and amorphous-to-amorphous transitions is presented. The pressure and time dependence of the a-GeO2 volume changes were measured during the high-pressure transformation. The transition occurs in a wide pressure region and the volume has logarithmic time dependence at a fixed pressure. Comparison of the solid-state amorphization and amorphous-to-amorphous transition is made.