The endosomal sorting complex required for transport (ESCRT) machinery is an assembly of protein subcomplexes (ESCRT I-III) that cooperate with the ATPase VPS4 to mediate scission of membrane necks from the inside. The ESCRT machinery has evolved as a multipurpose toolbox for mediating receptor sorting, membrane remodeling, and membrane scission, with ESCRT-III as the major membrane-remodeling component. Cellular membrane scission processes mediated by ESCRT-III include biogenesis of multivesicular endosomes, budding of enveloped viruses, cytokinetic abscission, neuron pruning, plasma membrane wound repair, nuclear pore quality control, nuclear envelope reformation, and nuclear envelope repair. We describe here the involvement of the ESCRT machinery in these processes and review current models for how ESCRT-III-containing multimeric filaments serve to mediate membrane remodeling and scission.