We re-examine solutions to the solar neutrino oscillations, decaying neutrinos and a cooler center of the sun. Comparison of the Homestake and Kamiokande II observations implies that low-energy neutrinos are more suppressed than high-energy, disfavoring the large-mass adiabatic MSW resonance and allowing us to exclude non-standard solar models with a simple reduction of core temperature. Diagonal ( sin 22θ - 0.004−0.5, Δm 2 ⋍ 0.08−10 meV 2) , vertical large-angle ( sin 2 ⋍ 0.6−0.9, Δm 2 ⋍ 0.08−2, 4−60 meV 2) , and part of the horizontal ( sin 22θ ⋍ 0.02−0.6, Δm 2 ⋍ 80 meV 2) MSW solutions are compatible with these data (meV = 10 −3 eV). The present SAGE results disfavor non-standard solar models and the horizontal MSW solution. Assuming ν e → ν μ conversion, we show that seesaw models of neutrino masses imply m ν μ = 0.3−9 meV, intermediate-scale symmetry breaking O(10 9–10 12) GeV, and a τ-neutrino mass with cosmological ramifications in some cases and laboratory or atmospheric ν μ − ν τ oscillations. While seesaw predictions for neutrino masses are model-dependent and subject to large uncertainties, we prove that leptonic mixing angles are similar to quark mixings for a wide range of models. We also present two specific seesaw models compatible with electroweak neutral current and proton decay constraints, including radiative corrections to the seesaw predictions.