Prion diseases are rare neurodegenerative diseases characterized by the conversion of the prion protein from its native state (PrP(C)) towards the so-called 'scrapie form', rich in β-strands. Computational approaches, here briefly reviewed, are instrumental to understand the intrinsic instability of PrP(C) fold and how the latter is affected by mutations, binding of metals as well as by different environmental conditions, such as pH and temperature. These studies also provide a structural basis for the binding of anti-prion compounds, which may block the conversion to the scrapie form and, consequently, may inhibit fibril formation.