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In this paper we review the use of iterative approaches for the numerical analysis of many electromagnetic scattering problems. In a variety of cases, iteration can be used to greatly extend the range of problems easily treated by a numerical solution of the conventional integral equations. Since the resulting matrix equations are not sparse, a special structure must be built into the discrete system in order to reduce the storage requirements. Two distinct discretization procedures are presented that provide the necessary structure when treating individual scatterers and infinite periodic arrays of scatterers. Since many additional problems of interest do not fall into this category, some recent efforts to treat more general problems are reported. In addition, we include a brief overview of preconditioning methods for the improvement of the convergence rates of iterative algorithms.