An abelian network is a collection of finite automata that live at the vertices of a graph and communicate via the edges. It produces the same output no matter in what order the automata process their inputs. Such a network can be viewed as an interacting particle system or as a model of asynchronous computation. This talk will survey the foundations of the subject, focusing on local-to-global principles and the halting problem for abelian networks. It will also feature pictures and conjectures about the intricate patterns that abelian networks create from simple local rules.