Amyloid fibers are highly organized protein aggregates that are associated with many fatal diseases. Prions represent a unique class of amyloid fibers that are distinguished by their infectivity and inheritability. In the yeast S. cerevisiae, there are several known prion forming proteins. Since the discovery of the first yeast prions in the early 1990s, they have provided a useful model system for studying the biology of prion proteins. While it has been determined that amino acid composition is important to prion formation, there has not yet been any quantitative study aimed at determining how composition promotes or inhibits prion formation. Without this knowledge, our understanding of the events that drive prion formation and our ability to identify new prion-forming proteins is severely limited. In this dissertation, we describe our experiments with the yeast prion protein Sup35p that have illuminated the sequence requirements for yeast prion formation. From these results, we conclude that: (i) amino acid composition, not primary sequence, is the major driving force behind yeast prion propagation, and (ii) prion formation occurs in domains characterized by relatively few prion promoting residues dispersed throughout an intrinsically disordered region.