**Scattering amplitudes andÂ gravitational waves**

I will describe an ongoing program to apply modern tools of perturbative quantum field theory to problems in classical general relativity relevant for current and future gravitational wave detectors. Recently, this effort culminated in the state-of-the-art calculation of the conservative two-body Hamiltonian at the fourth order in Newtonâ€™s constant, G^4, (or fourth post-Minkowskian order), and the G^3 radiated energy in binary black hole encounters. Computations made possible by harnessing methods such as the on-shell approach to scattering amplitudes, modern integration technology for collider observables, and effective field theory. I will also explain how the simplicity of the conservative problem allows a direct connection between the scattering amplitude and classical observables, as well as analytic continuation of the latter between bound and unbound trajectories.