All cells complete cell division by the process of cytokinesis. At the end of mitosis, eukaryotic cells accurately mark the site of division between the replicated genetic material and assemble a contractile ring comprised of myosin II, actin filaments and other proteins, which is attached to the plasma membrane. The myosin-actin interaction drives constriction of the contractile ring, forming a cleavage furrow (the so-called 'purse-string' model of cytokinesis). After furrowing is completed, the cells remain attached by a thin cytoplasmic bridge, filled with two anti-parallel arrays of microtubules with their plus-ends interdigitating in the midbody region. The cell then assembles the abscission machinery required for cleavage of the intercellular bridge, and so forms two genetically identical daughter cells. We now know much of the molecular detail of cytokinesis, including a list of potential genes/proteins involved, analysis of the function of some of these proteins, and the temporal order of their arrival at the cleavage site. Such studies reveal that membrane trafficking and/or remodelling appears to play crucial roles in both furrowing and abscission. In the present review, we assess studies of vesicular trafficking during cytokinesis, discuss the role of the lipid components of the plasma membrane and endosomes and their role in cytokinesis, and describe some novel molecules implicated in cytokinesis. The present review covers experiments performed mainly on tissue culture cells. We will end by considering how this mechanistic insight may be related to cytokinesis in other systems, and how other forms of cytokinesis may utilize similar aspects of the same machinery.