Appears in collection : Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday

The microlocal theory of sheaves has been introduced and developed by Kashiwara and Schapira in the 80’s, with motivations coming from the theory of D-modules. It has been applied some years ago to the study of symplectic geometry of cotangent bundles in papers of Nadler-Zaslow and Tamarkin. I will explain some results of these papers and subsequent works, in particular how we can associate a sheaf with any Hamiltonian isotopy of a cotangent bundle and how we can use such a sheaf to understand the topology of exact Lagrangian submanifolds.