This paper is a survey of E. Goles’ work on dynamical systems from the point of view of universality and computability. The models considered by E. Goles and his collaborators are presented: neural networks, reaction–diffusion automata, chip-firing games, sand piles, and artificial ants. Then, we recall the corresponding universality results. We also provide a classification of methods for proving universality and apply it to the aforementioned constructions.