The purpose of this conference is to bring to the fore current ideas on the possible mechanisms of superconductivity that determine the scale of the critical temperature and to debate which are the most promising directions of research, both to understand current materials and to identify promising directions for the discovery of new, higher temperature superconductors. These questions are central in condensed matter physics and will require the discovery of novel materials, the development of new experimental probes, and the solution of fundamental problems in the physics of strongly correlated systems.