Abstract: Plastic deformation of crystals is amenable to a variational formulation in the framework of continuum mechanics. At variance with the relatively well understood nonlinear elasticity, many modeling questions remain open, and the analysis of connection between models at different scales poses complex mathematical questions. This talk will focus on some recent mathematical result on the derivation of continuum models for dislocations from atomic-scale models and on the study of microstructure formation in scale-invariant continuum models for crystal plasticity.