  In this thesis we elaborate on two different aspects of the Effective Field
Theory (EFT) approach to a Binary Coalescing system in General Relativity (GR).
First, we consider the issue of hereditary effects in the Post-Newtonian (PN)
perturbative scheme, and we compute hereditary diagrams in the far zone region
up to 5PN order, using both Feynman and Schwinger-Keldysh formalism, comparing
our results with those appearing in literature. Then, we focus on the
Post-Minkowskian (PM) perturbative scheme, and we compute the bending angle of
a massless scalar field under the influence of a massive scalar in the EFT of
GR, up to one loop order in dimensional regularisation. Our analysis points to
the existence of relevant terms that were not accounted for in previous study,
which may modify the predictions for physical observables.
