As computers are built from ever smaller devices, with logical functions ultimately occurring statistically within individual molecules, issues of fault-tolerance become critical. Because at these scales transmission of information also becomes unreliable, local models such as cellular automata are often preferred for the formulation of fundamental results. Similarly, as global clocks cannot be relied upon, asynchronous operation must be considered. In this talk, I will informally describe the development of fault-tolerant cellular automaton models in one, two, and three dimensions. Emphasis will be on recent work, with Matt Cook and Peter Gacs, that has made use of topological concepts from the study of excitable media (which I learned as a boy from my father!) to develop new fault-tolerant asynchronous cellular automata.