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Precision predictions for binary mergers are essential for the nascent field of gravitational wave astronomy. The initial inspiral part can be treated perturbatively. We present results for the post-Minkowskian expansion of conservative binary dynamics, previously available only at the 2nd order for several decades, at the 3rd and 4th orders in the expansion. Our calculations are based on quantum field theory and use powerful methods developed in the modern scattering amplitudes program, as well as loop integration techniques developed for precision collider physics. Furthermore, we take initial steps in calculating radiative binary dynamics and obtain analytically the total radiated energy in hyperbolic black hole scattering, at the lowest order in G but all orders in velocity.