Multi-subunit ESCRT-III polymers together with the ATPase Vps4 have the unique ability to fission membrane necks from their luminal side, a process that is required for essential cellular functions like cell division and nuclear envelop maintenance. To decipher the mechanism of ESCRT-III membrane remodelling, I applied a vast array of in vitro reconstitution assays and electron microscopy, which revealed the following principles of ESCRT-III activity. First, membrane remodelling is driven by a polymerisation sequence which is determined by its subunits' biochemical features, second this polymerisation sequence is coupled to changes in polymer architecture and mechanical properties driving membrane deformation and fission, and third the nucleating complex likely determines the orientation of the initial polymer and subsequently generated membrane deformations. Moreover, by introducing the concept of flexible polymers which adapt their shape through dynamic changes of their subunit stoichiometry, my thesis proposes a new mechanism for membrane remodelling by polymerising proteins.