Three related electromagnetic scattering problems, namely, high frequency electromagnetic (EM) ray tracing, scattering feature extraction, and inverse scattering are studied in this dissertation. New approaches are presented to advance the state of the art in each of the areas. The presented study in electromagnetic ray tracing leads to an alternative ray tracing algorithm which can outperform the traditional algorithms for complex targets. The performance of the proposed techniques demonstrates their potential application to the study of high-frequency EM scattering prediction. Second, a genetic algorithm (GA)-based algorithm with an adaptive-feeding technique is developed to simultaneously extract both scattering centers and resonances. Scattering feature extraction algorithms are then developed with the consideration of the visibility of scattering centers. Inverse scattering problems with strong multiple scattering effects are also studied. A GA-based method is presented to invert the shapes with multiple scattering effects. An approach combining hybrid GA with the tabu list idea are then developed to further improve the performance of the GA-based inversion algorithms. / text