I will discuss the statement and proof of an Equivariant Main Conjecture (EMC) in the Iwasawa theory of arbitrary global fields. This will be followed by applications of the EMC (via Iwasawa co-descent) towards proving various well known conjectures on special values of global L-functions. In the process, an important role will be played by an explicit construction of ell-adic Tate sequences. This is based on joint work with Cornelius Greither (Munich).