During the past few decades, several new classes of superconductors have been discovered that do not appear to be related to traditional superconductors. The source of the superconductivity of these materials is likely different from the electron-ion interactions that are at the heart of conventional superconductivity. Developing a rigorous theory for any of these classes of materials has proven to be a difficult challenge and will remain one of the major problems in physics in the decades to come.