Ubiquitinated protein aggregates are hallmarks of a range of human diseases, including neurodegenerative, liver and muscle disorders. These protein aggregates are typically positive for the autophagy receptor p62. Whereas the ubiquitin-proteasome system (UPS) degrades shortlived and misfolded ubiquitinated proteins that are small enough to enter the narrow pore of the barrel-shaped proteasome, the lysosomal pathway of autophagy can degrade larger structures including entire organelles or protein aggregates. This degradation requires autophagy receptors that link the cargo with the molecular machinery of autophagy and is enhanced by certain posttranslational modifications of the cargo. In this review we focus on how autophagy clears aggregate-prone proteins and the relevance of this process to protein aggregate associated diseases.