Infrared-modified gravities and massive gravitons

We review some theoretical and phenomenological aspects of massive gravities in 4 dimensions. We start from the Fierz–Pauli theory with Lorentz-invariant mass terms and then proceed to Lorentz-violating masses. Unlike the former theory, some models with Lorentz violation have no pathologies in the spectrum in flat and nearly flat backgrounds and lead to an interesting phenomenology.