We will explain the construction of a Galois equivariant Goss-type L-function associated to an abelian t-motive and outline the formulation and proof of a Tamagawa Number Formula for its special values at positive integers. This generalizes to the t-motive and equivariant settings Taelman's celebrated class-number formula for Drinfeld modules. If time permits, we will show how the main result implies analogues of the  Brumer-Stark and Coates-Sinnott Conjectures for abelian t-motives. This is based on joint work with Ferrara, Green and Higgins.