This chapter presents a treatment of the mathematical aspects of continuum elastoplasticity. The focus is on rate‐independent material behavior, with the flow relations constructed within the framework of convex analysis. The basis for variational treatments of the problem is the versions of the flow relation that use the dissipation function or, alternatively, the yield surface with a normality law: these are referred to, respectively, as the primal and dual formulations. Both formulations are discussed, with emphasis on the former. Some results on the convergence of fully discrete approximations, using finite elements in space, are presented. The associated predictor–corrector algorithms are described, and their convergence behavior is discussed. A discussion of the large‐deformation theory includes an overview of the derivative‐free energetic formulation, due to Mielke and coworkers, and of which the primal formulation discussed in the small‐strain theory is a special case. Relevant results from functional analysis and function spaces are summarized at appropriate places in the presentation.