Consistent graviton theories

There has been a lot of progress recently in understanding what consistent graviton theories can be built in an effective field theory sense. This has led to the discovery of new graviton kinetic terms, potential interactions and ways of coupling matter to gravity. I will review and present this graviton theory space for local and Lorentz invariant theories. Along the way I will point out applications to cosmology, related discoveries of new dualities and symmetries, highlight which bits of theory space we already know to be unique and where there is still uncharted territory.