Closure phase is a number measured by triplets of Michelson interferometers that is completely independent of certain types of otherwise severe instrumental errors. In the 30 years since closure phase was invented, it has been applied to a diverse number of different problems in astronomical imaging. Methods based on the closure phase now allow imaging of complex objects in the presence of severe aberrations and are vital to the success of modern, high-resolution astronomical imaging both at radio and at optical wavelengths. Over the past 10 to 15 years, the concept of closure phase has been extended and generalized. One of the most important advances has been the development of automatic or self-calibration techniques. This article reviews closure phase methods and some of the many spin-offs and related ideas.