The basic problem of geodynamics is to explain the deep-seated processes which originate tectonic activity and earthquakes. To this end, the rheological conditions of materials within the Earth must be determined. The importance of the time factor and the difficulty of experimentally reproducing geodynamic conditions relevant to sub-lithospheric processes make it necessary to employ indirect evidence and to make heavy use of inference and analogy. Some constitutive equations for polycrystalline aggregates under high temperature and pressure and slow strain rate are examined and their consequences tested against occuring geodynamic processes. Sub-lithospheric deformation can be either continuous (slow redistribution of mass in the field of gravity, flow in the asthenosphere, convective movements in the mantle) or discontinuous (earthquakes). Two main questions are still unsolved in the rheology of continuous geodynamic processes, namely, the vanishing or non-vanishing value of the creep strength, and the linear or non-linear nature of the viscosity. The answer to these questions must be found in the interpretation of surface geological observations, particularly glacio-isostatic rebound, but no definite solution is available to date. In the rheology of discontinuous geodynamic processes, the very occurrence of sub-lithospheric earthquakes is puzzling. Ordinary Coulomb-Navier shear fracture (with or without pore fluid pressure) is not an adequate explanation for the occurrence of most seismic shocks. Other mechanisms that have been proposed range from creep instability and shear melting to dehydration and phase transition. Under high pressure and temperature conditions, continuous and discontinuous deformation are not mutually excluding processes, but they can occur in the same material and one may lead to the other. The most promising working hypothesis for sub-lithospheric shocks is some form of high-temperature creep instability leading eventually to rupture and sudden stress release.