Maintenance of proteome integrity (proteostasis) is essential for cellular and organismal survival. Various cellular mechanisms work to preserve proteostasis by ensuring correct protein maturation and efficient degradation of misfolded and damaged proteins. Despite this cellular effort, under certain circumstances subsets of aggregation-prone proteins escape the quality control surveillance, accumulate within the cell and form insoluble aggregates that can lead to the development of disorders including late-onset neurodegenerative diseases. Cells respond to the appearance of insoluble aggregates by actively transporting them to designated deposition sites where they often undergo degradation. Although several protein aggregate deposition sites have been described and extensively studied, key questions regarding their biological roles and how they are affected by aging remained unanswered. Here we review the recent advances in the field, describe the different subtypes of these cellular compartments and outline the evidence that these structures change their properties over time. Finally, we propose models to explain the possible mechanistic links between aggregate deposition sites, neurodegenerative disorders and the aging process.