A review of the present approaches to Cosserat plasticity and to its applications is presented, in comparison with the direct Theory of the Plastic Spin. In both theories, the classical rigid-plastic continuum with stress and strain rate as principal field quantities is generalized to also incorporate the relative “Plastic Spin”, ie, the average irreversible rotation of the microstructural elements (“grains” ) in a mesovolume, relative to the rotation induced by the field of point velocities or point displacements. Moreover, the Cosserat plasticity represents a complete, generalized continuum mechanical theory, where also the additional kinematic quantities, ie, the plastic spin and the internal twist are complemented by associate static quantities as, asymmetric stress or couple stress. While the direct Theory of the Plastic Spin is confined to non-isotropic materials, where the average rotation of the grains corresponds also to the rotation of the macrostructure, (texture) the Cosserat approach is also concerned with, and contemporarily even devoted to isotropic media. After presenting a general survey of the literature, experiments carried out with a generalized Couette flow, (for granular or rock-like materials) or in the torsion test, (for metals) are discussed showing that the Plastic Spin is an observable quantity generally different from zero even in an isotropic material. It can be predicted to the same extent, using the Cosserat plasticity as using any one of the much more complicated theories of crystal plasticity.