Since Drinfeld’s 1992 proposal to study the set-theoretic version of the Yang–Baxter equation, involutive solutions have attracted considerable attention. It is well known that to every non- degenerate involutive solution one can associate a permutation, referred to in the literature as the “diagonal permutation”. The aim of this talk is to show how this single permutation has a strong influence on the structure of (indecomposable) involutive set-theoretic solutions. Some of the results presented are part of a joint work with A. Kanrar.