The Born-Infeld model is an effective field theory of central importance describing the low-energy dynamics of massless gauge bosons on the world-volume of D-branes. Though it is in many ways an exceptional model of nonlinear electrodynamics, several aspects of the physics of the Born-Infeld model remain mysterious. In this talk I will explain how aspects of the model, obscured in the traditional formulation of Lagrangian field theory, are clarified by directly studying the on-shell S-matrix. In particular in 3+1-dimensions, classical Born-Infeld has an electromagnetic duality symmetry which manifests in tree-level scattering amplitudes as the conservation of a chiral charge. Whether this conservation law can be preserved under perturbative quantization is presently unknown. Using modern scattering amplitudes techniques, we have initiated a study of the S-matrix of Born-Infeld at one-loop. I will describe how generalized unitarity together with supersymmetric decomposition can be used to explicitly calculate infinite classes of one-loop amplitudes, and explain how the results are consistent with the existence of a quantum electromagnetic duality.