I will briefly recount the recent revival of the non-perturbative S-matrix Bootstrap.
Then I will explain how this (numerical) approach can be used to bound the space of Wilson coefficients in Effective Field Theories (EFT). I will focus on the application to supergravity in 10 spacetime dimensions (https://arxiv.org/abs/2102.02847). Remarkably, strongly coupled string theory seems to saturate the bounds imposed by Lorentz invariance, unitarity and causality.
At the end, we will discuss some of the many open questions in the field.