Inverse scattering techniques are aimed at recovering the profiles, positions and constitutive parameters of unknown objects belonging to an inaccessible region illuminated by known and successive probing fields from the measurements of the scattered field (i.e., the problem data) collected by a set of sensors in an external observation domain. Within such a framework, different methods have been proposed, based either on system matrix inversion or optimization approaches. Since multiple scattering effects cannot be neglegted, full non-linear formulations have to be used. The contrast field inversion (CFI) and the contrast source inversion (CSI) have been widely employed in a lot of practical applications (e.g., biomedical diagnosis or UXO and landmines detection, NDT/NDE, archeology, etc.).