  The most accurate model to describe the gravitational interaction is the
well-known theory of General Relativity. Several observational evidences
corroborate the legitimacy of the theory compared to the older Newtonian
gravity. General Relativity furthermore predicts the existence of gravitational
waves, i.e. spacetime ripples produced by accelerated masses. Thanks to a
connected network of interferometers called LIGO/Virgo, gravitational waves
from the coalescence of massive and compact astrophysical bodies have been
measured directly. These recent observations paved the way to a completely new
route to test the gravitational interaction. The possibility of using
gravitational waves to obtain a deeper understanding of open problems within
General Relativity motivates the work developed in this thesis. Each part is
essentially devoted to challenging the current model of gravitation, sometimes
including yet undiscovered new matter fields, and other times modifying the
theoretical framework of General Relativity.
  In the first part of this manuscript, I discuss the astrophysical
consequences of the presence of scalar fields permeating galaxies. A detailed
picture of the interaction of massive black holes and scalar dark matter
structures is provided. The second part is dedicated to the analysis of the
generation and propagation of gravitational waves. As an example, I examine the
close limit approximation as a promising tool to investigate the collision of
extreme compact objects. The last part of this thesis instead focuses on
unstable mechanisms around black holes and stars (scalarization and
vectorization), in two alternative models of gravitation.
