The recent results from the KAMIOKANDE II and BAKSAN solar neutrino experiments, if correct, imply that lepton flavour is not conserved. The Mikheyev-Smirnov-Wolfenstein (MSW) solution to the solar neutrino problem, which was first exposed by the HOMESTAKE Cl experiment, fully explains also these results if the electron neutrino is mixed with the muon neutrino or the tau neutrino with mixing parameters Δm2 ∼ 10-6cV-2 and sin22θ ∼ 4 × 10-2. This MSW solution can be tested with the new generation of solar neutrino experiments which will be able to detect both the predicted distortion of the spectrum of 8B solar ve's and the "missing" ve's that appear as vμ's or vτ's. Further evidence may be obtained from the day-night effect and from the flavour content of the neutronization burst from the birth of a neutron star in a nearby supernova. Moreover, the MSW solution combined with the seesaw mechanism for generating neutrino masses further suggests mve ∼ 10-8eV, mvμ ∼ 10-3cV, mvτ ∼ 10 cV, and sin22θ ∼ 4 × 10 -2 for vμvτ mixing. These predictions can be tested by previously proposed neutrino oscillation experiments at accelerators and by detecting neutrinos from a nearby supernova explosion. A tau neutrino with mvτ ∼ 10eV can account for most of the dark matter in the Universe and is a viable candidate for the hot dark matter scenario of the formation of large scale structure in the Universe.