I offer a leisurely introduction to the 'what', 'why', 'what exactly' and 'how' of my research, which revolves around groups acting on trees. Following a motivation of the subject by situating said groups within the broader theory of all groups, I explain the meaning of 'local' and 'global' in this context. With some examples of groups acting on trees at hand, I illustrate how, in general, 'local' actions have 'global' implications. (Credit to Alejandra Garrido for the title!)