Neutrino masses and oscillations: triumphs and challenges

The recent progress in establishing the existence of finite neutrino masses and mixing between generations of neutrinos has been remarkable, if not astounding. The combined results from studies of atmospheric neutrinos, solar neutrinos, and reactor antineutrinos paint an intriguing picture for theorists and provide clear motivation for future experimental studies. In this review, we summarize the status of experimental and theoretical work in this field and explore the future opportunities that emerge in light of recent discoveries.