  In this invited talk, I will review five basic concepts of Axiomatic
Rewriting Theory, an axiomatic and diagrammatic theory of rewriting started 25
years ago in a LICS paper with Georges Gonthier and Jean-Jacques L\'evy, and
developed along the subsequent years into a full-fledged 2-dimensional theory
of causality and residuation in rewriting. I will give a contemporary view on
the theory, informed by my later work on categorical semantics and
higher-dimensional algebra, and also indicate a number of current research
directions in the field.
