This article outlines several polycrystal formulations commonly applied for the simulation of plastic deformation and the prediction of deformation texture. It discusses the crystals of cubic and hexagonal symmetry that constitute the majority of the metallic aggregates used in technological applications. The article defines the basic kinematic tensors, reports their relations, and presents expressions for calculating the change in crystallographic orientation associated with plastic deformation. It surveys some of the polycrystal models in terms of the relative strength of the homogeneous effective medium (HEM). The article analyzes the anisotropy predictions of rolled face-centered-cubic and body centered-cubic sheets and presents simulations of the axial deformation of hexagonal-close-packed zirconium. The applications of polycrystal constitutive models to the simulation of complex forming operations, through the use of the finite element method, are also presented.