We present a calculation of the conservative two-body Hamiltonian of a compact
binary system including a spinning black hole.
We include up-to third order
corrections in Newton's constant $G$, all orders in velocity, and linear and
quadratic terms in spin. The results are obtained from the
classical limit of two-loop scattering amplitudes involving two massive scalars
and two massive spin-1 particles minimally coupled to gravity. We discuss the
usage of numerical techniques in our computation. In particular we show how the
numerical unitarity method is well suited to obtain results of relevance to the
physics program of current and future gravitational wave observatories.