In recent years, research in both mathematics and the applied sciences has produced a revolution in the understanding of nonlinear dynamical systems. Used videly in economics and other disciplines to model change over time, these systems are now known to be vulnerable to a kind of "chaotic," unpredictable behavior. This paper places this revolution in historical context, explains several of the important mathematical ideas on vhich it is based, and discusses some of its implications for a probabilistic interpretation of longrun economic phenomena.