The wave theory of light, and in particular the principle of interference, was formulated by Thomas Young in 1801. In the 20th century, the principle of interference was extended to the quantum mechanical wave functions describing matter. The phenomenon of quantum mechanical interference of different neutrino states, neutrino oscillations, has provided one of the most exciting developments in high energy particle physics of the last decade. Observations of the flavour oscillations of neutrinos produced by distant sources, such as from the core of the Sun, provide compelling evidence that neutrinos have mass. This article describes the main features and the most significant experimental observations of this unusual application of the principle of interference.