Fusion categories arise in several areas of mathematics and physics -conformal field theory, operator algebras, representation theory ofquantum groups, and others. They have a rich and fascinating structure. In this talk we will explain recent work, joint with Christopher Douglas and Noah Snyder, which ties this structure to the structure of 3-dimensional topological quantum field theories. In particular we show that fusion categories are fully-dualizable objects in a certain natural 3-category and identify the induced O(3)-action on the `space´ of fusion categories, as predicted by the cobordism hypothesis. In light of Hopkins´ and Lurie´s work on the cobordism hypothesis, this provides a fully local 3D TQFT for arbitrary fusion categories. Moreover by understanding various homotopy fixed point spaces, we will uncover how many familiar structures from the theory of fusion categories are given a natural explanation from the point of view of 3D TQFTs.