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Scattering amplitudes—which constitute some of the key ingredients that enable us to make predictions for particle physics experiments—have long been known to be constrained by physical principles such as causality and locality; however, the explicit form of these constraints has remained difficult to work out in practice. In this talk, I will give an overview of recent work that allows us to sidestep many of these difficulties, thereby allowing us to derive strong new constraints on the analytic structure of Feynman integrals and scattering amplitudes. I will then describe how these constraints can be fed into a bootstrap approach, via which the functional form of Feynman integrals can be determined from just knowledge of their singular behaviour.
