This is the preface of a special issue dedicated to the memory of Francisco Javier Sayas who passed away on April 2, 2019. The articles reflect Sayas' main research interests in the numerical analysis of partial differential equations, containing contributions on the scattering and propagation of acoustic and electromagnetic waves, and the analysis of discontinuous Galerkin schemes, boundary element methods, and coupled schemes. We discuss the main contributions of Sayas and give an overview of the results covered by this special issue.