This thesis presents some advancements in computational electromagnetics, focusing on integral equation methods for the solution of electromagnetic scattering problems. It explores numerical techniques and matrix operations that enhance the computational efficiency and accuracy necessary for practical applications: the analysis starts from the derivation of the BEM equations from the Maxwell's systems, continues exploring the most popular basis functions and discretization schemes, tackles the complexity issues that arise introducing fast solvers and preconditioning, investigates harmonic transforms and their behavior on non-regular domains, focuses on the recent preconditioning techniques relying on Laplacian filters, and finally introduces a novel approach to operator filtering. This work presents for most arguments both 2D and 3D formulations.