More than 20 human diseases are associated with protein misfolding, which results in the appearance of amyloids, fibrillar aggregates of normally soluble proteins. Such diseases are termed amyloid diseases, or amyloidoses. Of these, only prion diseases are transmissible. Amyloids of the prion type are known for lower eukaryotes. While mammalian prions cause neurodegenerative diseases, prions of lower eukaryotes are associated with some nonchromosomally inherited phenotypic traits. The review summarizes the results of studying the prions of yeast Saccharomyces cerevisiae and data obtained using S. cerevisiae as a model to investigate some human amyloidoses such as Alzheimer’s, Parkinson’s, Huntington’s, and prion diseases.