Abstract Endosomal sorting complexes required for transport-III (ESCRT-III) are thought to assemble in vivo inside membrane structures with a negative Gaussian curvature. How membrane shape influences ESCRT-III polymerization and conversely how ESCRT-III polymers shape membranes is still unclear. Here, we used human core ESCRT-III proteins, CHMP4B, CHMP2A, CHMP2B and CHMP3 to address this issue in vitro by combining membrane nanotube pulling experiments, cryo-electron microscopy, cryo-electron tomography and high-speed AFM. We show that CHMP4B filaments bind preferentially to flat membranes or to membrane tubes with a positive mean curvature. Both CHMP2B and CHMP2A/CHMP3 assemble on positively curved membrane tubes, the latter winding around the tubes. Although combinations of CHMP4B/CHMP2B and CHMP4B/CHMP2A/CHMP3 are recruited to the neck of pulled membrane tubes, they also reshape large unilamellar vesicles into helical membrane tubes with a pipe surface shape. Sub-tomogram averaging reveals that the filaments assemble parallel to the tube axis with some local perpendicular connections, highlighting the particular mechanical stresses imposed by ESCRT-III to stabilize the corkscrew-like membrane architecture. Our results thus underline the versatile membrane remodeling activity of ESCRT-III that may be a general feature of ESCRT-III required for all or selected cellular membrane remodeling processes.