The endosomal sorting complex required for transport-III (ESCRT-III) and VPS4 catalyze a variety of membrane-remodeling processes in eukaryotes and archaea. Common to these processes is the dynamic recruitment of ESCRT-III proteins from the cytosol to the inner face of a membrane neck structure, their activation and filament formation inside or at the membrane neck and the subsequent or concomitant recruitment of the AAA-type ATPase VPS4. The dynamic assembly of ESCRT-III filaments and VPS4 on cellular membranes induces constriction of membrane necks with large diameters such as the cytokinetic midbody and necks with small diameters such as those of intraluminal vesicles or enveloped viruses. The two processes seem to use different sets of ESCRT-III filaments. Constriction is then thought to set the stage for membrane fission. Here, we review recent progress in understanding the structural transitions of ESCRT-III proteins required for filament formation, the functional role of VPS4 in dynamic ESCRT-III assembly and its active role in filament constriction. The recent data will be discussed in the context of different mechanistic models for inside-out membrane fission.