In this article, we briefly describe human neurodegenerative diseases (NDs) and the experimental models used to study them. The main focus is the yeast Saccharomyces cerevisiae as an experimental model used to study neurodegenerative processes. We review recent experimental data on the aggregation of human neurodegenerative disease-related proteins in yeast cells. In addition, we describe the results of studies that were designed to investigate the molecular mechanisms that underlie the aggregation of reporter proteins. The advantages and disadvantages of the experimental approaches that are currently used to study the formation of protein aggregates are described. Special attention is given to the similarity between aggregates that form as a result of protein misfolding and viral factories—special structural formations in which viral particles are formed inside virus-infected cells. A separate part of the review is devoted to our previously published study on the formation of aggregates upon expression of the insect densovirus capsid protein in yeast cells. Based on the reviewed results of studies on NDs and related protein aggregation, as well as viral protein aggregation, a new experimental model system for the study of human NDs is proposed. The core of the proposed system is a comparative transcriptomic analysis of changes in signaling pathways during the expression of viral capsid proteins in yeast cells.