In this talk I will discuss our recent attempt https://arxiv.org/pdf/2410.23333 of understanding the QCD spectrum using the available experimental data. To do so, we developed a fit strategy that combines the S-matrix Bootstrap with non-convex optimization methods, and applied our algorithm to the case of \pi\pi scattering. The fitted amplitude correctly predicts the low energy ChiPT behavior, the experimental total cross sections at higher energy, and the physical spectrum up to 1.4 GeV. Surprisingly, the Bootstrap predicts an additional tetraquark state, not yet observed, and that is being investigated in the decay of the B+ -> pi+ p+ pi- at LHCb.