The paper focuses on the concept of plastic spin and its constitutive description in phenomenological theories for macroscopic large strain elastoplasticity. An overview is given of kinematic descriptions of the plastic spin and of constitutive relationships which have been proposed in the literature. Two important classes are distinguished: one in which plastic spin constitutive laws are derived from application of tensor representation theorems, and the second where they are derived from normality rules. Both classes are critically examined from a micromechanical point of view as well as from the standpoint of deterministic irreversible thermodynamics. The role of nonsymmetric state or structure variables in macroscopic plastic spin constitutive relations is emphasized and their origin is identified within the framework of crystal plasticity. The plastic spin in simple shear deformation processes is studied using various kinematic hardening models as well as a simple analytical multiple slip model proposed here.