The endosomal-sorting complex required for transport (ESCRT) is evolutionarily conserved from Archaea to eukaryotes. The complex drives membrane scission events in a range of processes, including cytokinesis in Metazoa and some Archaea. CdvA is the protein in Archaea that recruits ESCRT-III to the membrane. Using electron cryotomography (ECT), we find that CdvA polymerizes into helical filaments wrapped around liposomes. ESCRT-III proteins are responsible for the cinching of membranes and have been shown to assemble into helical tubes in vitro, but here we show that they also can form nested tubes and nested cones, which reveal surprisingly numerous and versatile contacts. To observe the ESCRT–CdvA complex in a physiological context, we use...