Prion proteins are infective amyloids and cause several neurodegenerative diseases in humans and animals. In yeasts, prions are expressed as cytoplasmic heritable determinants of a protein nature. Yeast prion [PSI], which results from a conformational rearrangement and oligomerization of translation termination factor eRF3, is used as an example to consider the structural--functional relationships in a potentially prion molecule, specifics of its evolution, and interactions with other prions, which form so-called prion networks. In addition, the review considers the results of modeling mammalian prion diseases and other amyloidoses in yeast cells. A hypothesis of proteomic networks is proposed by analogy with prion networks, involving interactions of different amyloids in mammals.