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Microlocal sheaf theory, mainly based on the notion of microsupport of sheaves, is a creation of M. Kashiwara and P. Schapira after M. Sato’s foundational ideas. Beyond its application to the study of systems of linear partial differential equations (D-modules), P. Schapira and his collaborators used microlocal sheaf theory to bring light and progress to many areas: analysis (Sobolev spaces), symplectic geometry and topology (connection with Tamarkin’s results), deformation by quantization, regular and irregular holonomic D-modules, Ind-sheaves, persistent homology, and the list is not exhaustive.

The aim of this journey is to present recent results which were influenced by Schapira’s work.