The discovery that neutrinos can convert from one flavour to another and therefore have nonzero masses is a major milestone for elementary particle physics. It represents compelling experimental evidence for the incompleteness of the Standard Model as a description of nature. Although the possibility of neutrino flavour change, i.e. neutrino oscillations, had been discussed ever since neutrinos were first discovered experimentally in 1956, it was only around the turn of the millennium that two convincing discoveries validated the actual existence of neutrino oscillations: in 1998, at Neutrino’98, the largest international neutrino conference series, Takaaki Kajita of the Super-Kamiokande Collaboration presented data showing the disappearance of atmospheric muon-neutrinos, i.e. neutrinos produced when cosmic rays interact with the atmosphere, as they travel from their point of origin to the detector. And in 2001/2002, the Sudbury Neutrino Observatory (SNO) Collaboration, led by Arthur B. McDonald, published clear evidence for conversion of electron-type neutrinos from the Sun into muon- or tau-neutrinos. These discoveries are of fundamental importance and constitute a major breakthrough. Neutrino oscillations and the connected issues of the nature of the neutrino, neutrino masses and possible CP violation among leptons are today major research topics in particle physics.