Wedge disclinations are rotational mismatches at the level of a crystal lattice observed in classes of Shape-Memory Alloys undergoing the austenite-to-martensite transformation and in crystal plasticity. In the first part of the talk I will describe the mathematical analysis of a variational model for systems of planar disclinations in the scenario of planar elasticity. In our theory disclinations emerge from kinematic incompatibility conditions prescribed at the atomistic level. We are interested in the asymptotics of the energy minima and minimizers, as the lattice spacing vanishes, which we compute exactly with Gamma-convergence. In the second part of the talk, I will show numerical computations based on a crystal (micro-) plasticity model which are examples of complex plastification rich in disclinations.