Cell division is a key event in the bacterial life cycle. It involves constriction at the midcell, so that one cell can give rise to two daughter cells. This constriction is mediated by a ring composed offibrous multimers of the protein FtsZ. However a host of additional factors is involved in the formation and dynamics of this "Z-ring" and this complicated apparatus is collectively known as the "divisome". We review the literature, with an emphasis on mathematical modelling, and show how such theoretical efforts have helped experimentalists to make sense of the at times bewildering data, and plan further experiments.