The detection of gravitational waves by LIGO/VIRGO in 2015 opened up a new era for multi-messenger astronomy. Precision theoretical predictions for gravitational wave signals require a combination of numerical and analytic perturbative calculations. We present a new framework for perturbative calculations, based on scattering amplitudes in quantum field theory and their classical limits. We use a wide range of tools in theoretical high-energy physics, including on-shell methods, the double copy, effective field theory, and advanced loop integration techniques. In our paper, the conservative dynamics of non-spinning black holes in a binary system is obtained at the third order in the gravitational constant for the first time. The result shows improved agreement with numerical relativity simulations compared with lower-order results. Since our breakthrough, a flurry of publications have extended our results to include the effect of spin, finite sizes, dissipation, and higher orders in perturbation theory.