An invitation to strong-field scattering

Scattering amplitudes in strong background fields provide an arena where perturbative and non-perturbative physics meet, with important applications ranging from laser physics to black holes, but their study is hampered by the cumbersome nature of QFT in the background field formalism. In this talk, I will try to convince you that strong-field scattering amplitudes contain a wealth of physical information which cannot be obtained with standard perturbative techniques, ranging from all-order classical observables to constraints on exact solutions. Furthermore, I will discuss how amplitudes in certain chiral strong fields can be obtained to all-multiplicity twistor and string methods.