In the last few years it has become clear that the S-matrix Bootstrap can provide precise quantitative bounds on the low energy Wilson coefficients compatible with the physical principles of causality, crossing symmetry and unitarity. In this talk I will present the first application of this formalism to quantum gravity theories. I will focus on the first non universal correction to the scattering amplitude in 10 dimensional maximal supergravity and compare the results with the String Theory predictions.
