In 1954, Fermi, Pasta and Ulam for the first time used a computer to understand the ergodic behavior of a dynamical system with many degrees of freedom, interesting to investigate the very foundations of Statistical Mechanics. Several baranches of physical and mathematical investigations started from that paper. The aim of the talk is to revisit, in the light of some recent numerical results, some significant ideas and conjectures on the model. In particular: (i) The presence, in the model, of (at least) two well separated time-scales: a short one, where only a few normal coordinates share energy, and a larger one, where energy equipartition among all normal modes occurs and the behavior of the model, in view of Statistical Mechanics, is regular. (ii) The fact that in the short time scale the dynamics of FPU, in spite of the partial energy sharing, is essentially integrable and closely follows the dynamics of the Toda model, while in the large time scale nonintegrability becomes manifest. The stability of results in the limit of large N (ideally, the search of uniformity in N) will play a central role. The gap between numerical insights and mathematical results, unfortunately, is large.