Amplitudes, Gravity and Classical Discontinuities

On-shell methods have revitalized interest in scattering amplitudes which have, in turn, shed some much needed light on the structure of quantum field theories. These developments have been warmly embraced by the particle physics community. Less so in the astrophyical and cosmological contexts. As part of an effort to address this imbalance, we illustrate these methods by revisiting two classic problems in gravity: gravitational light-bending and the vDVZ discontinuity of massive gravity.