  In this paper we discuss copositive tensors, which are a natural
generalization of the copositive matrices. We present an analysis of some basic
properties of copositive tensors; as well as the conditions under which class
of copositive tensors and the class of positive semidefinite tensors coincides.
Moreover, we have describe several hierarchies that approximates the cone of
copositive tensors. The hierarchies are predominantly based on different
regimes such as; simplicial partition, rational griding and polynomial
conditions. The hierarchies approximates the copositive cone either from inside
(inner approximation) or from outside (outer approximation). We will also
discuss relationship among different hierarchies.
