In this talk I will explore the space of two-to-two S-matrices in two-dimensional theories with a global O(N) symmetry, as restricted by the general principles of unitarity, crossing and analyticity. I will describe various features of the allowed space and identify some special points on its boundary with known integrable theories. Finally, I will present a useful dual formulation of the S-matrix bootstrap problem. Based on arXiv:1909.06495.