We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which ``particles'' embedded in space-time configurations carry information and interactions between particles effect information processing. This structural analysis can also be used to explain the evolutionary process by which the strategies were designed by the genetic algorithm. More generally, our goals are to understand how machine-learning processes can design complex decentralized systems with sophisticated collective computational abilities and to develop rigorous frameworks for understanding how the resulting dynamical systems perform computation.