We will discuss how amplitudes can be used to efficiently derive classical gravitational-wave observables characterizing black hole binary encounters. This technique is very flexible and can be applied to General Relativity, but also to its extensions and, in the spirit of Effective Field Theory, can be used to describe compact objects beyond Schwarzschild black holes. We will briefly discuss some recent applications to spinning black holes and to the subleading Post-Minkowsian waveforms.

The eikonal exponentiation provides a way to obtain the classical limit of gravity amplitudes and to calculate the total deflection in collisions of compact objects in the Post-Minkowskian (PM) regime. In this talk I will illustrate how the eikonal phase can be promoted to an operator combining elastic and inelastic amplitudes in order to account for gravitational-wave emissions. Up to 3PM order, this restores manifest unitarity and allows us to calculate the linear and angular momentum of the gravitational field after the collision, as well as the changes in the linear and angular momenta of the colliding bodies. In this way, one can explicitly check the corresponding balance laws. I will also explain how the framework easily accommodates both radiative effects, static effects, and linear tidal corrections.