Autophagy, a conserved mechanism for lysosomal degradation of cytoplasmic components, has received much attention recently owing to its importance in tissue remodelling and innate immunity, and because it has been proposed that autophagy protects against cancer and neurodegenerative diseases. Although much of the molecular machinery that mediates autophagy has been identified, there are still aspects of this pathway that remain enigmatic. One open issue is the involvement of endosomal sorting complex required for transport (ESCRT) proteins, which were originally identified for their role in sorting ubiquitylated membrane proteins into multivesicular bodies. In this Opinion article, we discuss four possible models that could explain the observation that autophagosomes accumulate in ESCRT-depleted cells. We propose that the involvement of ESCRT proteins in the fusion of autophagosomes with the endolysosomal system is the most plausible model.