We review recent progress using amplitudes methods to obtain new results for the conservative classical scattering of two massive black holes at order O ( 4 ). We include contributions from both potential and radiation modes which effect the conservative dynamics through the tail effect. We compute the 2 → 2 scattering amplitudes and extract the radial action through the amplitudeaction formula and derive the scattering angle. By matching we also obtain a Hamiltonian valid for arbitrary scattering trajectories.