The Nobel Prize in physics 2015 was awarded jointly to Takaaki Kajita and Arthur B. McDonald "for the discovery of neutrino oscillations，which shows that neutrinos have mass". One month later，seven physicists including Takaaki Kajita and Arthur B. McDonald，who make significant contribution in the research of neutrino oscillations， obtain the 2016 Breakthrough Prize in fundamental physics. Neutrino oscillation has become the focus of fundamental physics research. In this paper，using the principle of quantum mechanics，we simply describe the theory of neutrino oscillations and CP violation，and introduce several important scientific problems in the future neutrino research.