Gravitational waves provide a new probe into the strong-field regime of gravity. It is thus essential to identify the predictions of General Relativity on the nature of the two-body problem, and to contrast them to alternative theories. In this talk, I will review how Effective Field Theory formalisms allow to place constraints on gravitational theories. I will first introduce some of the tools used in the General Relativistic two-body problem, then show how one can adapt them to Scalar-Tensor theories. Finally, I will discuss the two-body problem in theories featuring Vainshtein screening, illustrating some of the main observable effects of screening in the Solar system, in binary pulsar trajectories and in gravitational wave emission.
Eugeny Babichev
