A survey of Hochschild cohomology for von Neumann algebras

In this paper we survey the field of Hochschild cohomology for von Neumann algebras. We describe the basic definitions and results without assuming background knowledge beyond some familiarity with von Neumann algebra theory. We offer no formal proofs of results, although we give detailed references to the literature. Instead, we concentrate on explaining the main techniques and how they are applied to obtain the significant theorems of the subject.