In the talk I will explain a joint work with M. Kashiwara and P. Schapira, inspired by results of D. Tamarkin. The microsupport of a sheaf on a manifold $M$, introduced by Kashiwara and Schapira, is a closed conic subset of the cotangent bundle of $M$ which indicates how far the sheaf is from being locally constant. It can be used to translate symplectic diffeomorphisms of the cotangent bundle into operations on sheaves on the base. In the talk I will recall quickly the definition and properties of the microsupport and explain how it can be used to recover non-displaceability results (Arnold’s conjecture).