Massive and Partially Massless Gravity

I will review recent developments in the non-linear theory of massive gravitons, or spin-2 fields.  On de Sitter space, there exists a special value for the mass of a graviton for which the linear theory propagates 4 rather than 5 degrees of freedom. If a fully non-linear version of the theory exists and can be coupled to known matter, it would have interesting properties and could solve the cosmological constant problem. I will describe evidence for and obstructions to the existence of such a theory, and recent developments.