On-shell methods are a key component of the modern amplitudes programme. By utilising the power of generalised unitarity cuts, and focusing on gauge invariant quantities, enormous progress has been made in the calculation of amplitudes required for theoretical input into experiments such as the LHC. Recently, a new experimental context has emerged in which scattering amplitudes can be of great utility: gravitational wave astronomy. Indeed, developing new theoretical techniques for tackling the two-body problem in general relativity is essential for future precision measurements. Scattering amplitudes have already contributed new state of the art calculations of post{Minkowskian (PM) corrections to the classical gravitational potential. The gravitational potential is an unphysical, gauge dependent quantity. This thesis seeks to apply the advances of modern amplitudes to classical gravitational physics by constructing physical, on-shell observables applicable to black hole scattering, but valid in any quantum eld theory. We will derive formulae for the impulse (change in momentum), total radiated momentum, and angular impulse (change in spin vector) from basic principles, directly in terms of scattering amplitudes. By undertaking a careful analysis of the classical region of these observables, we derive from explicit wavepackets how to take the classical limit of the associated amplitudes. These methods are then applied to examples in both QED and QCD, through which we obtain new theoretical results; however, the main focus is on black hole physics. We exploit the double copy relationship between gravity and gauge theory to calculate amplitudes in perturbative quantum gravity, from whose classical limits we derive results in the PM approximation of general relativity. Applying amplitudes to black hole physics o ers more than computational power: in this thesis we will show that the observables we have constructed provide particularly clear evidence that massive, spinning particles are the on-shell avatar of the no-hair theorem. Building on these results, we will furthermore show that the classically obscure Newman{Janis shift property of the exact Kerr solution can be interpreted in terms of a worldsheet e ective action. At the level of equations of motion, we show that the Newman{Janis shift holds also for the leading interactions of the Kerr black hole. These leading interactions will be conveniently described using chiral classical equations of motion with the help of the spinor helicity method familiar from scattering amplitudes, providing a powerful and purely classical method for computing on-shell black hole observables.