A famous theorem by Mukai (1988) provides a classification of all possible finite groups admitting a faithful action by symplectic automorphisms on some K3 surface. In 2011, in collaboration with Gaberdiel and Hohenegger, we proposed that a `physics version' of Mukai theorem should hold for certain two dimensional conformal quantum field theories, called non-linear sigma models (NLSM) on K3, that describe the dynamics of a superstring moving in a K3 surface. In particular, we provided a classification of all possible groups of symmetries of NLSM on K3, that commute with the N=(4,4) algebra of superconformal transformations. This result was later re-interpreted by Huybrechts as a classification of the finite groups of autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. In the last few years, the concept of symmetry group in quantum field theory has been vastly generalized. In the context of two dimensional conformal field theories, these developments suggest that the idea of `group of symmetries' should be replaced by `fusion category of topological defects'. We discuss how our previous classification result could be extended to include fusion categories of topological defects in non-linear sigma models on K3. The geometric interpretation of these categories is still mysterious. This is based on joint work in collaboration with Roberta Angius and Stefano Giaccari.