Macroautophagy, hereafter referred to as autophagy, is a complex process in which multiple membrane‐remodeling events lead to the formation of a cisterna known as the phagophore, which then expands and closes into a double‐membrane vesicle termed the autophagosome. During the past decade, enormous progress has been made in understanding the molecular function of the autophagy‐related proteins and their role in generating these phagophores. In this Review, we discuss the current understanding of three membrane remodeling steps in autophagy that remain to be largely characterized; namely, the closure of phagophores, the maturation of the resulting autophagosomes into fusion‐competent vesicles, and their fusion with vacuoles/lysosomes. Our review will mainly focus on the yeast Saccharomyces cerevisiae, which has been the leading model system for the study of molecular events in autophagy and has led to the discovery of the major mechanistic concepts, which have been found to be mostly conserved in higher eukaryotes.