in this talk we will discuss two central problems in algebraic number theory and their interconnections: explicit class field theory and the special values of l-functions.  the goal of explicit class field theory is to describe the abelian extensions of a ground number field via analytic means intrinsic to the ground field; this question lies at the core of hilbert's 12th problem.  meanwhile, there is an abundance of conjectures on the special values of l-functions at certain integer points.  of these, stark's conjecture has special relevance toward explicit class field theory.  i will describe two recent joint results with mahesh kakde on these topics.  the first is a proof of the brumer-stark conjecture. this conjecture states the existence of certain canonical elements in cm abelian extensions of totally real fields.  the second is a proof of an exact formula for brumer-stark units that has been developed over the last 15 years.  we show that these units together with other easily written explicit elements generate the maximal abelian extension of a totally real field, thereby giving a p-adic solution to the question of explicit class field theory for these fields.