Fusion categories are generalizations of the representation categories of finite groups. One source of new fusion categories are subfactors, inlusions of von Neumann algebras with trivial center. The search for exotic subfactors led to new interesting fusion categories. One can study chiral conformal field theory via so-called conformal nets. I will explain how conformal nets give rise to fusion categories via its (higher) representation theory. It is an open question if all unitary fusion categories come from conformal nets. I will give examples of families of fusion categories for which one can reconstruct a conformal net.