  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. This thesis aims at comparing the predictions of General Relativity
and scalar-tensor theories on gravitational observables using Effective Field
Theory techniques. In a first part, we show how simple scalar-tensor theories
can be embedded in the Non-Relativistic General Relativity approach to the
two-body problem and highlight their essential features. Furthermore, we study
the effects of a disformal coupling of the scalar on the two-body dynamics and
introduce a resummation technique. This new Non-Relativistic Scalar-Tensor
formalism will provide a basis for the study of the Vainshtein mechanism in
two-body configurations which is at the core of the second part of this thesis.
Finally, in a last part we devise an Effective Field Theory formalism adapted
to gravitational wave generation in theories featuring scalar hair, in the
extreme mass ratio regime.
