Understanding mechanical properties and their microscopic origins is fundamental for multiple fields in condensed matter research. They are controlled by defects, dislocations, diffusion, as well as microstructures, which are not trivial to study under extreme conditions. This chapter summarizes the last 25 years of advances in high pressure devices, x-ray measurements, and data interpretation capabilities for addressing the deformation and plasticity of materials under extreme conditions, from experiments in large volume presses or diamond anvil cells, texture and stress analysis in powder x-ray diffraction, multi-grain crystallography, to self consistent models of materials behavior. Examples of applications are then provided in the fields of geophysics and materials science along with perspectives for studies of plastic deformation under extreme conditions in the coming years.