Causality imposes constraints on the coupling constants in perturbative effective field theory, which have played a role in understanding scattering amplitudes, the a-theorem for renormalization group flows, and higher curvature corrections in quantum gravity. I will describe similar constraints on strongly interacting theories. In one limit, these constraints imply the averaged null energy condition, which links causality to the inequalities obeyed by quantum information. Then, in large-N conformal field theory, I'll describe how causality tightly constrains the stress tensor correlation functions, and points directly toward the emergence of Einstein gravity in the holographic dual.