  In this thesis, we study emission amplitudes for the class of nonlinear
processes of tails, which are processes of order $G_N^2$, and represent the
effect of scattering gravitational radiation off the static background
curvature, including not only mass tails but also the "failed" tails due to the
angular momentum of the source. As originally shown in our work, some of these
amplitudes present anomalies, which are then properly understood and corrected
with field theory tools which have straightforward counterpart in traditional
methods. We also investigate the relation between emission and self-energy
diagrams and, in particular, show that a correction to the anomalous
self-energy diagrams is necessary to correctly account for conservative terms
that arise from radiative processes. From this, we obtain the correct
contribution to the conservative 5PN stemming from the electric quadrupole
angular momentum failed tail, correcting previous results in the literature.
Besides this, we also compute for the first time the conservative contributions
from the angular momentum failed tail, for arbitrary multipole moments.
  Subsequently, we explore the natural higher-order extension (of order
$G_N^3$) of the mass tails, called tails of tails, for generic electric and
magnetic multipoles. As we will see, both long- and short-distance divergences
are encountered, which are then properly understood and dealt with in terms of
standard renormalization techniques. In this case, we are able to resum the
logarithmic contributions through the integration of the renormalization group
equation.
  Thus, in this thesis, we have extended the post-Newtonian perturbative
expansion in the particularly thorny region of processes involving the mixture
of radiative and potential modes.
