In this talk I will show how to isolate Effective Field Theory scattering amplitudes in the space of non-perturbative two-to-two amplitudes, using the S-matrix Bootstrap. I will discuss the phenomenology of the extremal amplitudes along the boundary which present zero/high-spin dominance, UV/IR dominance, Regge behaviour, etc. Finally I will show that this construction leads to novel bounds on operators of dimension less than or equal to six, and speculate about future applications to the SM EFT.