The recent observation of neutrino oscillations with atmospheric and solar neutrinos, implying that neutrinos are not massless, is a discovery of paramount importance for particle physics and particle astrophysics. This invited lecture discusses - hopefully in a way understandable also for the non-expert - the physics background and the results mainly from the two most relevant experiments, Super-Kamiokande and SNO. It also addresses the implications for possible neutrino mass spectra. We restrict the discussion to three neutrino flavours (nu_e, nu_mu, nu_tau), not mentioning a possible sterile neutrino.
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