To electromagnetically test damaged anisotropic multilayers like composite panels of aeronautic and automotive industry is a difficult question: one needs fast and robust algorithms yielding images amenable to end-users’ decision about potential defects in both High-Frequency (HF) cases (dielectric materials) and Low-Frequency (LF) cases (conductive materials). Besides, it is important to get the results in close-to-real-time. Yet one also needs accurate responses of the multilayers, sound or damaged, to exterior sources at the forward modeling stage. The latter is considered via a Fourier-based Method of Moments applied onto an exact contrast-source integral equation involving the dyadic Green’s function of the layering, and via a first-order solution involving it as well as depolarization tensors of the assumed defects if small enough vis-à-vis the wavelength (HF) or skin depth (LF). The presentation will have two aims: to recapitulate most recent achievements, with emphasis on the fast calculation of the Green’s function when the dipole sources lie far away from the origin, yielding a fast-oscillating spectrum; to appraise most novel results obtained by standard and improved MUltiple SIgnal Classification (MUSIC) algorithms for small multiple defects in weak interaction, while investigating MUSIC beyond its expected domain of application, for somewhat larger spherical defects.