A review of a set of approaches for electromagnetic imaging that exploit the `a-priori' information on the sparseness of the unknown scatterers to define computationally-efficient inversion procedures is presented. The imaging problem is formulated within the Contrast Source formulation and successively recast into the Bayesian Compressive Sampling (BCS) framework by modeling the scatterers geometry with a hierarchical sparseness prior. A set of preliminary results is provided to assess the features and potentialities of the proposed approach.