Endocytosis describes the processes by which proteins, peptides and solutes, and also pathogens, enter the cell. Endocytosed material progresses to endosomes. Genetic studies in yeast, worms, flies and mammals have identified a set of universally conserved proteins that are essential for early‐to‐late endosome transition and lysosome biogenesis, and for endolysosomal trafficking pathways, including autophagy. The two Vps‐C complexes CORVET (class C core vacuole/endosome tethering) and HOPS (homotypic fusion and vacuole protein sorting) perform diverse biochemical functions in endocytosis: they tether membranes, interact with Rab GTPases, activate and proof‐read SNARE assembly to drive membrane fusion, and possibly attach endosomes to the cytoskeleton. In addition, several of the CORVET and HOPS subunits have diversified in metazoans, and probably form additional specialized complexes to accomodate the higher complexity of trafficking pathways in these cells. Recent studies offer new insights into the complex relationships between CORVET and HOPS complexes and other factors of the endolysosomal pathway. Interactions with V‐ATPase, the ESCRT machinery, phosphoinositides, the cytoskeleton and the Rab switch suggest an intricate cooperative network for endosome maturation. Accumulating evidence supports the view that endosomal tethering complexes implement a regulatory logic that governs endomembrane identity and dynamics.