Additional challenges stem from the fact that these processes have fast evolutions (relative to the large-scale deformation), are controlled by local factors, and are often anisotropic. For instance, rocks deforming at high stress conditions are subjected to changes in the microstructure, like grain size reduction or development of layering. However, these changes have an extremely heterogeneous spatial distribution starting at the mm scale (Fig. 1). In rocks deforming in presence of melts (or fluids), strong feedbacks develop, which result in both segregation of the fluid phase and further strain localization. All these processes result in heterogeneity of the mechanical behavior of the rocks at the mm to the meter scale. They cannot be explicitly modeled in geodynamical simulations with 100s of meters to km-scale spatial discretization and are therefore represented by average rheological behaviors. This upscaling by homogenization (averaging) results in “loosing” the heterogeneity in mechanical behavior, which is the natural seed for strain localization. By consequence, ad-hoc weakening has to be introduced to produce highly localized deformation in subduction zones, to initiate rifting, or to model convection with continental plates.