Protein filaments are used in different ways to organise other molecules in space and time within cells. Some proteins form filaments that couple hydrolysis of nucleotides to their polymerisation cycle in order to power the directed movement of other molecules, these filaments are termed cytomotive. Only members of the actin and tubulin superfamilies are known to form cytomotive filaments. The protein FtsZ, a homologue of eukaryotic tubulins, forms cytomotive filaments that are used in almost all bacteria and many archaea to organise cell division. Here I show using X-ray crystallography and electron cryomicroscopy (cryoEM) that FtsZ switches conformation when it polymerises into filaments. I then show using cryoEM that this conformational switch is likely needed for recognition of filaments by the widely conserved filament cross-linking protein ZapA. I also present the development of a high- throughput assay for detection of better FtsZ inhibitors, which uses principles derived from the structural studies. Finally, I demonstrate that the conformational switch upon polymerisation seen in FtsZ is conserved within the tubulin superfamily, that actin superfamily members also exhibit a conserved conformational switch upon polymerisation, and that having such a switch explains the coupling of kinetic and structural polarities required for cytomotivity of the filaments formed by these protein families.