Atmospheric and Solar Neutrino Masses and Abelian Flavor Symmetry

Recent atmospheric and solar neutrino experiments suggest that neutrinos have small but nonzero masses. They further suggest that mass eigenvalues have certain degree of hierarchical structures, and also some mixing angles are near-maximal while the others are small. We first survey possible explanations for the smallness of neutrino masses. We then discuss some models in which the hierarchical pattern of neutrino masses and mixing angles arises as a consequence of U(1) flavor symmetries which would explain also the hierarchical quark and charged lepton masses.