The main focus of this work is to contribute to the development of iterative solvers applied to the method of moments solution of electromagnetic wave scattering problems. In recent years there has been much focus on current marching iterative methods, such as Gauss-Seidel and others. These methods attempt to march a solution for the unknown basis function amplitudes in a manner that mimics the physical processes which create the current. In particular the forward backward method has been shown to produce solutions that, for some twodimensional scattering problems, converge more rapidly than non-current marching Krylov methods. The buffered block forward backward method extends these techniques in order to solve three-dimensional scattering problems. The convergence properties of the forward backward and buffered block forward backward methods are analysed extensively in this thesis. In conjunction, several means of accelerating these current marching methods are investigated and implemented. The main contributions of this thesis can be summarised as follows: ² An explicit convergence criterion for the buffered block forward backward method is specified. A rigorous numerical comparison of the convergence rate of the buffered block forward backward method, against that of a range of Krylov solvers, is performed for a range of scattering problems. ² The acceleration of the buffered block forward backward method is investigated using relaxation. ² The efficient application of the buffered block forward backward method to problems involving multiple source locations is examined. ² An optimally sized correction step is introduced designed to accelerate the convergence of current marching methods. This step is applied to the forward backward and buffered block forward backward methods, and applied to two and three-dimensional problems respectively. Numerical results demonstrate the significantly improved convergence of the forward backward and buffered block forward backward methods using this step.