Cellular Automata (CA) based simulations are widely used in a great variety of domains, fromstatistical physics to social science. They allow for spectacular displays and numerical predictions. Are they forall that a revolutionary modeling tool, allowing for “direct simulation”, or for the simulation of “the phenomenon itself”? Or are they merely models "of a phenomenological nature rather than of a fundamental one”? How do they compareto other modeling techniques? In order to answer these questions, we present a systematic exploration of CA’s various uses.