Bacteria and archaea usually divide symmetrically by formation of a septum in the middle of the cell. A key event in cell division is the assembly of the FtsZ ring. FtsZ is the prokaryotic homolog of tubulin and forms polymers in the presence of guanine nucleotides. Here, we specifically address the polymerization of FtsZ and the role of nucleotide hydrolysis in polymer formation and stabilization. Recent structural and biochemical results are discussed and a model for FtsZ polymerization, similar to that for tubulin, is presented.