The microlocal theory of constructible sheaves

The microlocal point of view was introduced by M. Sato in the 1960s for studying partial differential equations. It was then adopted by M. Kashiwara and P. Schapira and developed into a systematic theory in the context of sheaves on manifolds. The theory has since had applications in many fields, including partial differential equations, symplectic geometry, geometric Langlands, and exponential sums. In this talk, I will explain the basic ingredients of this theory, and discuss recent development of its analogues in the contexts of étale sheaves on algebraic varieties and rigid analytic varieties.