In this talk, which concerns groups acting on trees, I will describe joint work with Colin Reid in which we develop a ‘local action’ complement to classical Bass–Serre theory. We call this the theory of local action diagrams. This theory addresses a limitation of Bass–Serre theory that frequently occurs when one tries to construct novel examples of “large” groups acting on trees. This limitation has been particularly troublesome in the rapidly developing theory of totally disconnected and locally compact groups. To highlight the significance of our theory, I will describe how we can use it to obtain a complete classification of all group actions on trees that have Tits’ Independence Property (P) and further consequences.