This talk examines the fundamental role of scattering resonances in a range of important applications, including target identification and the evaluation of time-domain transients for complex two- and three-dimensional scattering configurations. It further demonstrates how these resonances can be leveraged to develop highly efficient time-domain solvers and identification methodologies. Emphasis is placed on high-order, high-performance methodologies designed to efficiently address large-scale scattering structures with high accuracy.