The degradation of misfolded proteins is essential for cellular homeostasis. Misfolded proteins are normally degraded by the ubiquitin-proteasome system (UPS), and selective autophagy serves as a backup mechanism when the UPS is overloaded. Selective autophagy mediates the degradation of harmful material by its sequestration within double-membrane organelles called autophagosomes. The selectivity of autophagic processes is mediated by cargo receptors, which link the cargo to the autophagosomal membrane. The p62 cargo receptor (SQSTM1) has a main function during the degradation of misfolded, ubiquitylated proteins by selective autophagy; here it functions to phase separate these proteins into larger condensates and tether them to the autophagosomal membrane. Recent work has given us crucial insights into the mechanism of action of the p62 cargo receptor during selective autophagy and how its activity can be integrated with the UPS. We will discuss these recent insights in the context of protein quality control and the emerging concept of cellular organization mediated by phase transitions. © 2018. Published by The Company of Biologists Ltd.