Abstract: Describing the low-energy physics of a given confining gauge theory is in general a very difficult problem. Instead, one can proceed with a bootstrap approach to carve out the space of effective field theories that are compatible with some set of assumptions. In this talk, I will discuss how to implement this approach in the context of pion scattering, targeting large N QCD. I will first review the constraints stemming from the basic assumptions of crossing and unitarity, and I will then motivate some minimal assumptions beyond these which yield very suggestive bootstrap solutions. Time permitting, I will discuss how one can also exploit the chiral anomaly to derive novel inhomogeneous bounds.