Abelian processes are a family of stochastic (or deterministic) message-passing processes on a graph that are abelian in the sense that the order of messages doesn’t affect the final state. This gives them algebraic structure and makes them more amenable to study. Examples are internal diffusion-limited aggregation, activated random walk, or the abelian sandpile model. This is a collection of three papers about the final state of some abelian process, or about the number of steps it takes to reach that state.