A brief review of research on pressure solution is given. The mechanisms of pressure solution and Coble creep are discussed. Deformation by diffusive mass transfer processes is generally accompanied by grain boundary sliding and this will have important effects on the textures and microstructures produced during deformation. Experiments using relaxation testing seem promising in allowing access to the slow strain rates necessary to observe pressure solution phenomena. The thermodynamics of non-hydrostatically stressed solids is discussed and an analysis of possible diffusion paths in rocks is presented. Evaluation of theoretical rate equations for pressure solution and Coble creep indicates that pressure solution in fine-grained quartz and calcite rocks may give rise to geological strain rates at temperatures from 200–350°C. Coble creep is expected to give rise to geological strain rates in fine-grained galena at low temperatures and also in fine-grained calcite rocks at temperatures around 350°C. The chemistry of natural rock pressure solution systems is expected to have significant effects and needs further detailed study. Further research is needed to elucidate the nature and role of grain boundaries during diffusive mass transfer. Pressure solution phenomena are important in the compaction behaviour of some petroleum reservoir rocks and perhaps in some faults where sliding is accommodated by pressure solution.