Recent developments in the consistency and existence of massive theories of gravity has led to a resurgence of interest in their relevance for cosmology. The recent direct detection of gravitational waves by Ligo has also provided a constraint on the possible existence of a mass for the graviton. I have been developing a better understanding of massive theories of gravity, and the constraints upon the graviton mass that can be obtained from a host of astrophysical, gravitational and cosmological observations, as well as to look for possible extensions of these theories, for instance by adding supersymmetry. In a parallel work with my collaborators we have discovered an infinite number of previously unknown constraints that apply to effective theories of gravity that come from extending 1960’s work on the analytic S-matrix, relying on the assumption that a given effective field theory, which describes the low energy world, admits a consistent high energy description which is local, unitary and Lorentz invariant. These constraints should prove very useful to future developments of effective field theories for cosmology.