Many proteins can misfold into beta-sheet-rich, self-seeding polymers (amyloids). Prions are exceptional among such aggregates in that they are also infectious. In fungi, prions are not pathogenic but rather act as epigenetic regulators of cell physiology, providing a powerful model for studying the mechanism of prion replication. We used prion-forming domains from two budding yeast proteins (Sup35p and New1p) to examine the requirements for prion formation and inheritance. In both proteins, a glutamine/asparagine-rich (Q/N-rich) tract mediates sequence-specific aggregation, while an adjacent motif, the oligopeptide repeat, is required for the replication and stable inheritance of these aggregates. Our findings help to explain why although Q/N-rich proteins are relatively common, few form heritable aggregates: prion inheritance requires both an aggregation sequence responsible for self-seeded growth and an element that permits chaperone-dependent replication of the aggregate. Using this knowledge, we have designed novel artificial prions by fusing the replication element of Sup35p to aggregation-prone sequences from other proteins, including pathogenically expanded polyglutamine.