Prions are the proteinaceous infectious agents responsible for the transmission of prion diseases. The main or sole component of prions is the misfolded prion protein (PrP(Sc)), which is able to template the conversion of the host's natively folded form of the protein (PrP(C)). The detailed mechanism of prion replication and the high-resolution structure of PrP(Sc) are unknown. The currently available information on PrP(Sc) structure comes mostly from low-resolution biophysical techniques, which have resulted in quite divergent models. Recent advances in the production of infectious prions, using very pure recombinant protein, offer new hope for PrP(Sc) structural studies. This review highlights the importance of, challenges for and recent progress toward elucidating the elusive structure of PrP(Sc), arguably the major pending milestone to reach in understanding prions.