Many of the long-standing mysteries in theoretical physics today are, in one way or another, related to gravity. This fact is a very powerful motivation for trying to improve our knowledge on gravitational interactions and plausible extensions of general relativity, in particular to understand their consistency with basic physical principles like unitarity, locality and causality. In this talk I will show how such fundamental principles lead to positivity constraints on scattering amplitudes in theories with a massless graviton in the spectrum in four spacetime dimensions, and how they allow us to tackle current puzzles in quantum gravity and modified gravity theories. For instance, these new bounds imply that extremal black holes are self-repulsive, thus providing an S-matrix proof of the celebrated weak gravity conjecture. I will also discuss how these bounds affect modifications of gravity relevant for cosmology, as well as some future directions of investigation.
