Neutrinos have mass - So what?

In this brief review, we discuss the new physics unveiled by neutrino oscillation experiments over the past several years, and discuss several attempts at understanding the mechanism behind neutrino masses and lepton mixing. It is fair to say that, while significant theoretical progress has been made, we are yet to construct a coherent picture that naturally explains nonzero, yet tiny, neutrino masses and the newly revealed, puzzling patterns of lepton mixing. We discuss what the challenges are, and point to the fact that more experimental input (from both neutrino and "non-neutrino" experiments) is dearly required - and that new data is expected to reveal, in the next several years, new information. Finally, we draw attention to the fact that neutrinos may have only just begun to reshape fundamental physics, given the fact that we are yet to explain the LSND anomaly and because the neutrino oscillation phenomenon is ultimately sensitive to very small new-physics effects.