Theoretical Overview of Neutrino Properties

I give an overview of some basic properties of massive neutrinos. The first part of this talk is devoted to three fundamental questions about three known neutrinos and to their flavor issues -- the mass spectrum, mixing pattern and CP violation. The second part of this talk is to highlight a few hot topics at the frontiers of neutrino physics and neutrino astrophysics, including the naturalness and testability of TeV seesaw mechanisms at the LHC, effects of non-standard interactions on neutrino oscillations, flavor distributions of ultrahigh-energy cosmic neutrinos at neutrino telescopes, collective flavor oscillations of supernova neutrinos, flavor effects in thermal leptogenesis, the GSI anomaly and Moessbauer neutrino oscillations, and so on. I finally make some concluding remarks for the road ahead.