Obtaining the low-energy EFT of a given large-N confining gauge theory is in general a very difficult problem. Instead, one can proceed by carving out the space of allowed EFTs using the constraints on scattering amplitudes that follow e.g. from unitarity and crossing symmetry. In this talk I will review how to do this in the context of pion physics, with large-N QCD as our target. I will discuss what bounds this imposes on the chiral Lagrangian, and what theories saturate the bounds. I will end by discussing how a mixed system of pions and photons allows us to input symmetries and anomalies into the bootstrap, paving the way for bootstrapping large N QCD.