When classical electromagnetic or acoustic modes of a waveguide interact with plane waves that impinge upon the guide, resonant scattering occurs. The resonance is similar to the "Fano resonance" in quantum mechanics. We will present the model of Fano and then show a rigorous derivation for classical electromagnetics that generalizes the Fano resonance for very general periodic structures. Joint work with N. Ptitsyna and S. Venakides.