The history of superconductivity has been referred to as the history of quantum mechanics. Following the first observation of the phenomenon in 1911, it took nearly five decades to arrive at the now-famous Bardeen-Cooper-Schrieffer (BCS) theory of "low Tc" superconductivity. Even more person-years have, however, gone into research on the mechanism of "high Tc" superconductivity, which was discovered in 1986, and about which there is no consensus to date.

In the first part of this talk I will briefly discuss the surprises and challenges that make the high Tc problem such a formidable one. The difficulty arises not merely in the high critical temperatures of the superconductors but also in the dominant repulsive interaction among the charge carriers, which make the simple BCS theory inapplicable to these systems. Following this, I will point out that there is now general agreement that similar repulsive interactions characterize many other unconventional superconductors, and there exists therefore an entire class of systems that lie outside the scope of the BCS theory. I will then focus on one such family of materials, organic charge-transfer solids, and discuss our recent advances towards understanding the mechanism of superconductivity in these. It is conceivable that this particular mechanism is applicable to correlated electron superconductors in general.