**Abstract**

Gravitational waves are propagating ripples in space-time geometry, produced bythe accelerated motion of massive astrophysical objects or by cosmologicalsources, and they have been first observed by the Advanced Laser Interferometer Gravitational Observatory (LIGO) in September 2015, when the signal from a pairof coalescing black holes were detected. Since then, during the observationrun 1, 2 and 3 which spanned overall about 2 years, a total of 90 events originated by compact binary coalescences have been detected. At the time of writing (March 2020) the 4th observation run of LIGO/Virgo/KAGRA is being prepared, as it is scheduled to start around the end of this year 2022. Within the field of gravitational wave physics my line of research aims at maximizing the physics and astrophysics output of detections, which depend critically on faithful gravitational waveforms. Coalescing binaries are privileged systems to study the two-body problem in classical gravity, as they represent a mine of information for fundamental gravity, astrophysics and cosmology. Their signal is determined by the dynamics ruling the motion of the binary system, which for now coincides with General Relativity. In particular recent works have shown that the computation of the General Relativistic, hence classical, dynamics of massive bodies can benefit from the input from Quantum Field Theory scattering amplitude computation program, which has been so powerful and insightful in unveiling deep structures of elementary particle physics and my goal is to work to connecting the amplitude program to the physics of gravitational waves. Better knowledge of the gravitational dynamics will impact research fields beyond fundamental physics. On the astronomy side it is now of fundamental importance to understand the main formation channel of black hole binaries, and to shed light on this problem it is crucial to have a better estimation of the source astrophysical parameters, including spins, which also requires better modeling, especially ofthe sub-dominant gravitational modes. On the cosmological side binary black holes are known to be standard sirens, which can be used to have an unbiased measure of luminosity distance, whichis one of the two ingredients, together with redshift (which however is not measurable from gravitational observations only), to determine the cosmic expansion history, hence the matter content of the universe. Different type of analysis must be used when dealing with electromagnetically bright standard sirens, i.e. systems whose redshift is measurable viaits electromagnetic emission, or dark ones, in the latter case the redshift value can only be inferred statistically, via correlation with astrophysical information carried by galaxy catalogs and/or expected redshift distribution of sources. In both cases, though, the precision of cosmological parameter estimation can be improved by the concurrent measure of the impact of dark energy on the growth factor of large scale structures. (AU)