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 has been hampered by many technical and conceptual issues. 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 for high-multiplicity processes using techniques from integrability and string theory.
