All solar, atmospheric, reactor and long-baseline accelerator neutrino data can be explained by postulating that there are three neutrinos, that these have non-zero, non-identical masses, and that the neutrino mass eigenstates are not aligned with the neutrino flavor eigenstates. In this talk, I first briefly discuss experimental data-along with possible interpretations-that may already point to physics beyond the minimal massive neutrino paradigm. I then discuss the possibility that there are more neutrinos than the old standard model called for. These so-called sterile neutrinos are a very simple and often quite useful extension of the standard model, and may prove to be a potentially testable side-effect of the physics responsible for neutrino masses. 10th International Workshop on Neutrino Factories, Super beams and Beta beams June 30-July 5 2008 Valencia, Spain * Speaker. † It is a pleasure to thank the Local Organizing Committee of NuFact'08 for putting together an excellent program in a very relaxing and inspiring venue. I also thank Carlos Peña-Garay and the Scientific Program Committee for the invitation. This work is sponsored in part by the US Department of Energy Contract DE-FG02-91ER40684.