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              <p>This chapter provides a comprehensive presentation of some  qualitative methods associated with inverse  3D electromagnetic scattering problem from inhomogeneous and anisotropic  media. We first discuss the problem in the framework of so-called Born  approximation, that leads to a linearisation of the inverse problem. We second  present and analyze the application of the Linear Sampling Method to the full non linear  problem using multistatic data at a given frequency. We especially focus on a generalization of this method based on an  exact characterization of the inclusion shape in terms of the available  data. We then discuss the closely related interior transmission problem and  associated transmission eigenvalues. We complement each chapter with some  open challenging questions as well as references for further readings.</p>
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