My talk will describe recent progress in the program to apply modern tools for computing scattering amplitudes to problems in classical general relativity. These include the calculation of the (potential contributions to the) conservative two-body Hamiltonian at the fourth order in Newton’s constant, G^4, as well as the G^3 radiated energy in binary black hole encounters and elliptical orbits. I will focus on two developments that enabled these calculations. The first of these is an improved understanding of the connection between classical scattering amplitudes and the semiclassical on-shell action. The other is the application of modern loop integration methods, such as canonical differential equations and reverse unitarity, to the kind of integrals relevant for the computation of classical quantities. Finally, I will comment on certain universal features that can be observed by comparing the dynamics of black holes in classical Einstein gravity and supergravity.