SummaryProtein and lipid transport along the endolysosomal system of eukaryotic cells depends on multiple fusion and fission events. Over the past few years, the molecular constituents of both fission and fusion machineries have been identified. Here, we focus on the mechanism of membrane fusion at endosomes, vacuoles and lysosomes, and in particular on the role of the two homologous tethering complexes called CORVET and HOPS. Both complexes are heterohexamers; they share four subunits, interact with Rab GTPases and soluble NSF attachment protein receptors (SNAREs) and can tether membranes. Owing to the presence of specific subunits, CORVET is a Rab5 effector complex, whereas HOPS can bind efficiently to late endosomes and lysosomes through Rab7. Based on the recently described overall structure of the HOPS complex and a number of in vivo and in vitro analyses, important insights into their function have been obtained. Here, we discuss the general function of both complexes in yeast and in metazoan cells in the context of endosomal biogenesis and maturation.