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I will present recent work on high-precision computations of the scattering of spinning black holes in the post-Minkowskian (PM) approximation. Working in a weak-field regime, black holes or other compact objects are described in an effective field theory framework as point-like particles. In this setting, the PM corrections can be arranged in a loop expansion in close analogy to high-precision computations in particle physics. I will present state-of-the-art results at the 5PM order corresponding to 4-loop Feynman integrals. At this order many physical effects are present: dissipation of energy and angular momentum, tail effects and time non-locality, and Wilson couplings distinguishing black holes and neutron stars. Several methods of quantum field theory (QFT) may advantageously be imported to this (classical) two-body problem as done, for example, in the worldline QFT formalism which I will present and which greatly streamlines classical perturbative computations. A main application of these results is in gravitational wave physics which requires a resummation of the perturbative results. Here, I will briefly showcase recent work on spinning, post-Minkowskian effective-one-body resummations and comparisons with numerical relativity.