Electromagnetic probing of natural and/or man-made structures that are buried in subsoil or hidden within walls or other known obstacles certainly remains a challenging task yet it is in need for a range of applications that can go from most traditional civil engineering applications to novel interrogations, like on the estimation of root systems of trees and biomass evaluation, as one among many examples. This multi-authored multi-laboratory contribution is based on existing as well as just being started works on the above issue endeavored in them. It will go in some depth into examples being drawn from this research, with peculiar emphasis on two joint issues, computational imaging (in a weak scattering as well as a fully non-linear realm) and optimal antenna design. Then, it will attempt to point out challenges ahead, from modeling to experiments in controlled enough situations