The main conjecture in classical Iwasawa Theory makes a link between special values of l-adic L-functions and certain Iwasawa modules which are the char o analogues of the l-adic realizations (Tate modules) of Jacobians of smooth projective curves over finite fields of char p different from l. From this vantage point, the classical Main Conjecture in Iwasawa Theory is the exact analogue of Weil's Theorem expressing global L-functions in char p in terms of characteristic polynomials of the geometric Frobenius morphism acting on the l-adic realizations of the corresponding Jacobian varieties. In this talk, we extend this analogy in two directions: First, replacing Jacobians by 1-motives and L-functions by equivariant L-functions, we formulate and prove (joint work with C. Greither) an Equivariant Main Conjecture in char p, linking special values of equivariant L-functions to the action of the geometric Frobenius on the l-adic realizations of the ensuing 1-motives. Second, a char 0 analogue of the geometric Equivariant Main Conjecture is formulated, which links special values of equivariant l-adic L-functions to the Iwasawa theoretic analogues of the l-adic realizations of Deligne's 1-motives; and we show how this new Main Conjecture implies the classical conjectures on global L-values due to Brumer-Stark, Gross and Coates-Sinnott.