Abstract. In the recent past the S-matrix Bootstrap has provided precise quantitative bounds on the low energy Wilson coefficients compatible with causality, crossing symmetry and unitarity for some class of EFTs associated with the low energy QCD dynamics.  In this talk I will discuss the first application of this formalism to quantum gravity theories.  I will focus on the first non universal correction to the flat space scattering amplitude of 10 dimensional supergravity particles, and compare the results with the String Theory predictions.