The purpose of this work is to exploit the algorithmic formulation of models for multiscale inelastic materials whose behavior is influenced by the evolution of inelastic microstructure and the corresponding material or internal lengthscales. The models for extended crystal plasticity are based on the formulation of rate potentials whose form is determined by (i) energetic processes via the free energy, (ii) kinetic processes via the dissipation potential, and (iii) the form of the evolution relations for the internal-variable-like quantities upon which the free energy and dissipation potential depend. Examples for these latter quantities are the inelastic local deformation or dislocation densities as GNDs. Different algorithmic implementations are discussed, namely the algorithmic variational approach and the dual mixed approach.