Topological defects in quantum field theory can be understood as a generalised notion of symmetry, where the operation is not required to be invertible. Duality transformations are an important example of this. By considering defects of various dimensions, one is naturally led to more complicated algebraic structures than just groups. So-called 2-groups are a first instance, which arise from invertible defects of codimension 1 and 2. Without invertibility one arrives at so-called "fusion categories”. I would like to explain how one can "gauge" such non-invertible symmetries in the case of topological field theories, and I will focus on results in two and three dimensions. This talk is based on joint work with Nils Carqueville, Vincentas Mulevicius, Gregor Schaumann, and Daniel Scherl.
