Research on bacterial cell division has recently gained renewed impetus because of new information about peptidoglycan assembly and about specific cell-division genes and their products. This paper concerns aspects of cell division that specifically concern the peptidoglycan. It is shown that upon division, peptidoglycan assembly switches from lateral wall location to the cell centre, that assembly takes place at the leading edge of the invaginating constriction, that the mode of glycan strand insertion changes from a single-stranded mode to a multi-stranded mode, and that the initiation of division (in contrast to its continuation) requires penicillin-insensitive peptidoglycan synthesis (PIPS). A membrane component X (possibly FtsQ) is proposed to coordinate PIPS with the cell division-initiating protein FtsZ. It is suggested that a largely proteinaceous macromolecular complex (divisome) at the leading edge of constriction encompasses three compartments (cytoplasm, membrane and periplasm). The composition of this complex is proposed to vary depending on whether division is being initiated or completed.