Studies of anisotropic materials and the discovery of various novel and unexpected phenomena under shock loading has contributed significantly to our understanding of the behavior of condensed matter. The variety of experimental studies for isotropic materials displays systematic patterns, giving basic insights into the underlying physics of anisotropic shock wave modeling. There are many similarities and significant differences in the phenomena observed for isotropic and anisotropic materials under shock-wave loading. Despite this, the anisotropic constitutive equations must represent mathematical and physical generalization of the conventional constitutive equations for isotropic material and reduce to the conventional constitutive equations in the limit of isotropy. This article presents the current state of the art in the constitutive modeling of this fascinating field.