In view of the recent observations of gravitational-wave signals from black-hole mergers, classical black-hole scattering has received considerable interest due to its relation to the classical bound-state problem of two black holes inspiraling onto each other. In this talk I will discuss the link between classical scattering of spinning black holes and quantum scattering amplitudes for massive spin-s particles. Starting at first post-Minkowskian (PM) order, I will explain how the spin-exponentiated structure of the relevant tree-level amplitude follows from minimal coupling to Einstein's gravity and in the \(s \rightarrow \infty \) limit generates the black holes' complete series of spin-induced multipoles. The resulting scattering function will be shown to encode in a simple way the known net changes in the black-hole momenta and spins at 1PM order and to all orders in spins. Then I will move on to the new results at 2PM order for the case of aligned black holes' spins and discuss the current state of the art for classical black-hole scattering.