I will present some recent work on axions that highlights the quantized nature of its couplings to gauge bosons. Anomaly matching allows connecting far UV with the IR, making it possible to probe fundamental properties of theories with low energy experiments. As applications, I will describe new observables in the CMB that can tell us about the fundamental unit of electric charge, and show that tabletop experiments probing axion-photon couplings can be a probe of grand unification.