Even though the combined laboratory, astrophysical and cosmological evidence implies that neutrinos have masses, neutrinos provide only a small cosmic dark matter component. The study of solar neutrinos provides important information on nuclear processes inside the Sun as well as on matter densities. Moreover, supernova neutrinos provide sensitive probes for studying supernova explosions, neutrino properties and stellar collapse mechanisms. Neutrino-nucleus reactions at energies below 100 MeV play essential roles in core-collapse supernovae, explosive and r-process nucleosynthesis, as well as observation of solar and supernova neutrinos by earthbound detectors. On the other hand, recent experimental data of high-energy extragalactic neutrinos at 1 PeV open a new window to probe non-standard neutrino properties, such as resonant effects in the oscillation probability.