Focus is on modeling of the electromagnetic behavior of complex dispersive, anisotropic structures, with in mind damaged fiber-based, flat composite panels as in aeronautic and automotive industries. The goal is to image these panels if damaged (defects are of many sorts, like delaminations, cracks, inclusions) via proper probes, to get reliable information on these defects. Yet, before imaging, one has to accurately and quickly compute the fields or pertinent associated quantities in ways versatile enough in terms of materials, sources, frequencies, etc. Also, one should devise both large-scale models assuming homogenized anisotropic media characterized by permittivity tensors and small-scale ones wherein each layer in the panels looks like a superposition of periodic rods (bundles of fibers) to achieve better and broader understanding. The presentation encompasses all such aspects while pinpointing also what is ahead for imaging solutions.