Endogenous yeast amyloids that control heritable traits and are frequently used as models for human amyloid diseases are termed yeast prions. Yeast prions, including the best studied ones ([PSI⁺] and [URE3]), propagate via intimate interactions with molecular chaperones. Different yeast prions exhibit differential responses to changes in levels, functionality or localization of the components of chaperone machinery. Here, we provide additional data confirming differential effects of chaperones (and specifically, Hsp40s) on yeast prions and summarize current knowledge of the mechanisms underlying chaperone specificities. Contrary to frequent statements in literature, overproduction of the Hsp104 chaperone antagonizes both [PSI⁺] and [URE3] prions, while overproduction of the Hsp70-Ssa1 chaperone antagonizes [URE3] prion only in some, but not in all strains. Recently, we demonstrated that the relocalization of a fraction of the Hsp40 chaperone Sis1 from the cytosol to the nucleus by the chaperone-sorting factor Cur1 exhibits opposite effects on [PSI⁺] and [URE3] prions. We suggest that the response of prions to changes in Sis1 localization represents a combination of the effects of Sis1 shortage on fragmentation of prion aggregates and on malpartition of prion aggregates during a cell division. Differences in sensitivity of prion fragmentation to Sis1 and in relative inputs of fragmentation and malpartition in prion propagation result in opposite effects of Sis1 relocalization on [PSI⁺] and [URE3].