Cell division facilitated by a contractile ring is an almost universal feature across all branches of cellular life, with the notable exception of higher plants. In all organisms that use a contractile ring for cell division, the process of cytokinesis can be divided into four distinct stages. Firstly, the cell needs to specify a location at which to place the cell division ring to ensure proper separation of the cell contents into two daughter cells. Secondly, the cell needs to be able to transport all the necessary components to this region, and construct the cell division ring reliably and efficiently. Thirdly, the cell division ring needs to generate contractile stress in a regulated manner, to physically cleave the mother cell into two daughter cells. Finally, the ring must be disassembled to allow for the final abscission and separation of the daughter cells. In this review, we will discuss some of the proposed mechanisms by which eukaryotic cells are able to complete the first three of these stages. While there is a good understanding of the mechanisms of division site specification in most organisms, and the mechanisms of actomyosin ring formation are well studied in fission and budding yeast, there is relatively poor understanding of how actomyosin interactions are able to generate contractile stresses during ring constriction, although a number of models have been proposed. We also discuss a number of myosin motor-independent mechanisms that have been proposed to generate contractile stress in various organisms.