The Nobel Prize in Physics 2015 was awarded to Takaaki Kajita and Arthur B. McDonald, who led experiments on atmospheric and solar neutrinos, respectively. These experiments discovered neutrino oscillations, which showed that neutrinos have mass. These seminal results revealed new physics beyond the standard model of particle physics. An introduction is given to these experiments and the relevant physics in the hope that readers would get an overall impression of research on neutrinos and a proper appreciation of the knowledge acquired and the methodology used by physics.