  The primary tool for analysing groups acting on trees is Bass--Serre Theory.
It is comprised of two parts: a decomposition result, in which an action is
decomposed via a graph of groups, and a construction result, in which graphs of
groups are used to build examples of groups acting on trees. The usefulness of
the latter for constructing new examples of `large' (e.g. nondiscrete) groups
acting on trees is severely limited. There is a pressing need for new examples
of such groups as they play an important role in the theory of locally compact
groups. An alternative `local-to-global' approach to the study of groups acting
on trees has recently emerged, inspired by a paper of Marc Burger and Shahar
Mozes, based on groups that are `universal' with respect to some specified
`local' action. In recent work, the authors of this survey article have
developed a general theory of universal groups of local actions, that behaves,
in many respects, like Bass--Serre Theory. We call this the theory of local
action diagrams. The theory is powerful enough to completely describe all
closed groups of automorphisms of trees that enjoy Tits' Independence Property
(P).
  This article is an introductory survey of the local-to-global behaviour of
groups acting on trees and the theory of local action diagrams. The article
contains many ideas for future research projects.
