The structures of the infectious prion protein, PrP(Sc), and that of its proteolytically truncated variant, PrP 27-30, have evaded experimental determination due to their insolubility and propensity to aggregate. Molecular modeling has been used to fill this void and to predict their structures, but various modeling approaches have produced significantly different models. The disagreement between the different modeling solutions indicates the limitations of this method. Over the years, in absence of a three-dimensional (3D) structure, a variety of experimental techniques have been used to gain insights into the structure of this biologically, medically, and agriculturally important isoform. Here, we present an overview of experimental results that were published in recent years, and which provided new insights into the molecular architecture of PrP(Sc) and PrP 27-30. Furthermore, we evaluate all published models in light of these recent, experimental data, and come to the conclusion that none of the models can accommodate all of the experimental constraints. Moreover, this conclusion constitutes an open invitation for renewed efforts to model the structure of PrP(Sc).