I.S. Cohen's 1946 paper "On the structure and ideal theory of complete local rings" established strong classification theorems for complete noetherian local rings in full generality. We will focus on an important case of these classification theorems, that of complete noetherian local rings which contain a field. We will show that such a ring R is the homomorphic image of a power series ring in finitely many variables over a field and is also a module-finite extension of such a ring. In this way, these power series rings play a role analogous to that of polynomial rings in the context of finitely generated algebras over a field. We will also show that, if R is furthermore assumed to be regular, then R is itself isomorphic to one of these power series rings. Speaker(s): Carsten Sprunger (University of Michigan Ann Arbor)