Protein aggregation is a continuous process in our cells. Some proteins aggregate in a regulated manner required for different vital functional processes in the cells whereas other protein aggregates result from misfolding caused by various stressors. The decision to form an aggregate is largely made by chaperones and chaperone-assisted proteins. Proteins that are damaged beyond repair are degraded either by the proteasome or by the lysosome via autophagy. The aggregates can be degraded by the proteasome and by chaperone-mediated autophagy only after dissolution into soluble single peptide species. Hence, protein aggregates as such are degraded by macroautophagy. The selective degradation of protein aggregates by macroautophagy is called aggrephagy. Here we review the processes of aggregate formation, recognition, transport, and sequestration into autophagosomes by autophagy receptors and the role of aggrephagy in different protein aggregation diseases.