The goal of this project was to develop a new generation of fast, robust, and accurate methods for solving the equations of electromagnetic scattering in realistic environments involving complex geometry. During the six year performance period including a one-year no cost extension, we have made definitive progress in this direction. We have constructed new integral representations for scattering from perfect conductors and dielectrics that work across the frequency spectrum, are immune from low-frequency breakdown, and can be applied to surfaces of arbitrary genus. We have designed new quadrature methods QBX for quadrature by expansion which are high-order, efficient and easy to use on arbitrarily triangulated surfaces. The resulting discretized integral equations are compatible with fast multipoleaccelerated solvers and will form the basis for high fidelity modeling software that can handle complicated, electrically large objects in a manner that is sufficiently fast to allow design by simulation.