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More than fifty years after the publication of the early work on conduction and dielectric breakdown of solids, we are still unable to describe quantitatively the electrical response of these materials. During this period of time, concepts derived from semiconductor physics have been transposed to the case of insulating solids, and among them, to polymers. Alternative descriptions have been proposed as well. In spite of this, there is still no agreement on how to describe charge transport and there is still some controversy as regards the applicability of semiconductors physics to the case of disordered insulating materials and in particular to polymers used in electrical engineering applications. The last twenty years have been marked by the publication of excellent review papers summarizing the physical concepts available to describe charge transport. Enormous steps forward have been achieved as regards computing facilities and our ability to spatially map the space charge, quantitatively, inside dielectric materials. We consider these two factors as fundamental in providing possibilities for developing sound models of charge transport, by using the basis of fundamental knowledge that has been accumulated in the previous years, and by coupling up-to-date techniques in experiments and in simulation. In this paper, which is not a review of either the published work on modeling or of new concepts in dielectric physics, we emphasize recent progress in the field of atomistic and macroscopic modeling and we discuss challenges based on such approaches that, we think, constitute a direction for future research.