In terms of shock-compression characteristics, minerals of geophysical interest are placed in a class of materials which, because of some rather unique Hugoniot and shock-compression properties, are classified as brittle solids. The physical processes responsible for these shock-wave properties are not yet well established. However, recent experimental observations and theories based on localized, nonhomogeneous shear deformation and a transient nonuniform thermal state appear to provide a reasonable qualitative picture. In the present work, some of the terminal and tranient shock-compression features observed in brittle solids are reviewed with particular emphasis on Hugoniot release-wave measurements. The possibility of instabilities in the laws governing shear deformation leading to observed heterogeneous deformation is considered, and although an elementary model is treated, the method shows promise of predicting the material and kinematic properties governing occurrence, growth, and frequency of localized deformation features. Transient stress wave calculations in crystalline quartz demonstrate how the kinematic environment governing instability growth is established under shock-wave compression. In addition, the transient nonuniform thermal state resulting from heterogeneous deformtion is shown to provide a possible explanation for the observation of both 'fluidlike' and 'solidlike' shock release waves depending on the competing properties of thermal diffusion, melting temperature, and degree of thermal localization. The analysis shows a striking difference between those minerals which do, and do not, undergo a shock-induced phase transition and leads to speculated similarities between the kinetics of shock-induced phase transformation in brittle solids and the kinetics of thermal detonation in explosives.