An equisingular heritage of Bernard Teissier

We give a brief and partial overview of Bernard Teissier’s work in complex equisingularity theory, and a perspective on its legacy; in particular, we focus on the development of the theory in the real and the non-Archimedean contexts. Our aim is not to go into technical details, but, hopefully, rather to give a flavour of the forms taken by these developments, while providing enough definitions and references to give the reader access to old and new reference articles in the field.