Abstract: This paper reviews our recent progress in further improving the numerical simulation capabilities and enhancing their engineering application abilities with some advanced and efficient numerical methods which are all developed following the multilevel fast multipole algorithm (MLFMA) framework. Among them, the phase extracted (PE) basis functions developed for scattering analysis of extra-large targets (particularly of cavities), the combined field integral equation with electric and magnetic currents (JMCFIE) used for simulation of hybrid conductor and radar absorbing structures, the multilayer thin dielectric sheets (TDS) approximation methods for antenna and radar radome modeling, as well as the accelerated Cartesian expansion (ACE) method contributing to rapid calculation of multi-scale structures are introduced and demonstrated with some numerical applications. Finally, a concise discussion and explorations are drawn to the present challenges and possible remedy strategy for electromagnetic simulation and its engineering application.