In the 1970s and early 1980s Stark developed a remarkable conjecture aimed at interpreting the first non-vanishing derivative of an Artin L-function L_{K/k, S}(s, \chi) at s=0 in terms of the arithmetic properties of the Galois extension of global fields K/k. Work of Tate, Chinburg, and Stark himself has revealed far reaching applications of Stark's Conjecture to Hilbert's 12-th Problem and the theory of Galois module structure of groups of units and ideal-class groups. In his search for new examples of Euler Systems, Rubin has formulated in 1994 a strong version ("over Z", in Tate's terminology) of Stark's Conjecture for abelian L-functions of arbitrary order of vanishing at s=0. Our study of the functorial base-change behavior of Rubin's Conjecture led us to formulating a seemingly more natural Stark-type conjecture "over Z". We will discuss and provide evidence for this new statement, as well as briefly describe the main goals of the conjectural program initiated by Stark.