The Challenge of Unconventional Superconductivity
  During the past few decades, several new classes of superconductors have been discovered. Most of these do not appear to be related to traditional superconductors. As a consequence, it is felt by many that for these materials, superconductivity arises from a different source than 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 continue to be one of the major problems in physics in the decades to come. 
M. R. Norman
cond-mat.supr-con