Abstract: A cellular automata is, for the purposes of this presentation, a sequence of colorings of $V(G)$ that proceeds according to a homogeneous local update rule where $G$ is a locally finite graph and the set of colors used is finite. The behavior of these models is often very complex. It is not surprising that there are few rigorous mathematical results concerning cellular automata. However, there are theorems concerning the global behavior of some (sufficiently simple) models that have combinatorial proofs. In this lecture we discuss two such theorems and mention some open combinatorial questions that have arisen in the study of cellular automata.