Being deeply connected to signalling, cell dynamics, growth, regulation, and defence, endocytic processes are linked to almost all aspects of cell life and disease. In this review, we focus on endosomes in the classical endocytic pathway, and on the programme of changes that lead to the formation and maturation of late endosomes/multivesicular bodies. The maturation programme entails a dramatic transformation of these dynamic organelles disconnecting them functionally and spatially from early endosomes and preparing them for their unidirectional role as a feeder pathway to lysosomes.