I will discuss a far reaching conjectural link between special values of global and p-adic L-functions which unifies and refines some classical conjectures of Stark, Gross, and Rubin. I will report on progress in establishing this link emerging from my joint work with Greither in equivariant Iwasawa theory and relate that to recent results in this area due to Dasgupta and his collaborators. The (Wednesday) RTG Colloquium lecture will be introductory in nature. It will be followed by a more technical (Thursday) Number Theory Seminar lecture where the main techniques and results will be explained in more detail.