The strongly anisotropic rheology of olivine and pyroxene single grains, associated to polycrystal microstructures, constitutes a key feature affecting the dynamics of the Earth's upper mantle. High pressure deformation experiments carried out on olivine single crystals under synchrotron radiation, together with estimations of lattice friction based on first-principle calculations, show a transition from easy [100] to easy [001] slips as pressure and temperature (thus depth) increases. Besides dislocation glide, diffusion related deformation mechanisms such as dislocation climb, diffusional creep, and grain boundary sliding cannot be completely ruled out. Since their behavior is poorly known, they are grouped into a single isotropic viscous component. We input these elementary deformation mechanisms into a mean-field homogenization scheme (second-order self-consistent scheme of Ponte-Castaneda) to assess the respective activation of deformation mechanisms and microstructure evolution (crystallographic texture) of olivine and olivine-pyroxene polycrystalline aggregates, for several flow path representative of in situ deformation.