The six articles in this EMS volume provide an overview of a number of contemporary techniques in the study of the asymptotic behavior of partial differential equations. These techniques include the Maslov canonical operator, semiclassical asymptotics of solutions and eigenfunctions, behavior of solutions near singular points of different kinds, matching of asymptotic expansions close to a boundary layer, and processes in inhomogeneous media. Asymptotic expansions are one of the most important areas in the theory of partial differential equations. Readers should find the wide variety of approaches of interest.