Beginning with a discussion of the nature of the FPU problem and the results of the original simulations, including the remarkable “FPU recurrences,” I show how a continuum limit analysis clarifies the nature of these recurrences and leads directly to the equations to which the concept of solitons was first applied. I next establish the existence of deterministic chaos in the FPU problem and discuss briefly recent attempts to clarify the transition between the solitonic and chaotic regimes. I will show how investigations derived from the FPU problem have clarified several outstanding problems in physics, including anomalous heat transport in real low-dimensional materials, the existence of “intrinsic localized modes, and the origins of statistical mechanics.