Cell division in most bacteria and archaea is facilitated by a constricting ring structure, containing the protein FtsZ. FtsA anchors FtsZ to the membrane and FtsZ recruits other proteins of the divisome, the machine that divides the inner and outer cell membrane and the cell wall. During division, the FtsZ ring decreases in diameter through an unknown mechanism, eventually separating the two daughter cells. Here we show the organisation of FtsZ filaments in constricting E. coli cells and in liposomes being constricted in vitro by a ring of FtsZ and FtsA filaments, all using electron cryotomography. In E. coli cells, mutant FtsZ(D212) forms bands of double filaments that form complete rings around the cell's perimeter. Over-expression of FtsZ and FtsA in E. coli leads to extra division sites that separate off minicells and hence function in division. We therefore performed in vitro reconstitution of constriction by encapsulating FtsZ and FtsA proteins on the inside of liposomes generated from E. coli lipids. This leads to spontaneous dumbbell-shaped membrane constrictions that co-localise with rings of filaments. Electron cryotomography of the ring structures formed allowed detailed visualisation of the constrictions as well as complete tracing of the helical paths of the filaments. Since in vitro reconstitution of FtsZ-based constriction does not require energy from nucleotide turnover and constrictions occur only at sites where rings have formed, we put forward a mechanism of FtsZ-based cell constriction that is driven by filament sliding and condensation.