  We report here on two works on Lorentz invariant massive gravity. In the
first part, we derive the decoupling limit of massive gravity on de Sitter,
relying on embedding de Sitter into an higher dimensional Minkowski spacetime.
This enables us to identify the unique candidate for a partially massless
gravity theory, in which only four degrees of freedom propagate, although
further work showed that this property does not hold beyond the decoupling
limit. In the second part, we study the fate of the Vainshtein mechanism in the
minimal model of massive gravity, in which we show the limits of the often used
assumptions of staticity and spherical symmetry.
