Modular tensor categories are rich mathematical structures. They are important in the study of 2D conformal field theory, arising as categories of modules for rational vertex operator algebras. The orbifold construction A-> A^{G}  for a finite group G is a fundamental method for producing new theories from old. In the case the orbifold theory is also rational, the construction of the modular tensor category Rep(A^{G}) directly from the modular tensor category Rep(A) with G-action is a categorical construction called gauging. In this talk, we will explain gauging for abstract modular tensor categories equipped with a G-action (not necessarily arising from a CFT). There are cohomological obstructions to performing this construction in the abstract setting which do not arise in the setting of VOA orbifolds. Unfortunately these obstructions are difficult to compute, making the abstract theory of gauging difficult to work with in practice. However, we will present results showing these obstructions vanish for permutation actions on tensor powers of an arbitrary modular category tensor category. This verifies a conjecture of Mueger, and nullifies proposed counterexamples to the conjecture that all modular categories arise from rational conformal field theory. Based on joint work with Terry Gannon.