We present a class of modified theories of gravity in which vacuum energy can be screened or degravitated. We argue that any such theory must reduce at the linearized level to a theory of a massive or resonance graviton. The immediate implication is that there are new degrees of freedom, associated with the extra polarizations of the graviton. Phenomenologically, this results in a fifth force which is suppressed in regions of high density but becomes relevant on large (>Mpc) scales. We discuss the implications for cosmological evolution and structure formation.