The ultimate goal of all signaling pathways in cytokinesis is to control the mechanical separation of the mother cell into two daughter cells. Because of the intrinsic mechanical nature of cytokinesis, it is essential to understand fully how cell shapes and the material properties of the cell are generated, how these shapes and material properties create force, and how motor proteins such as myosin-II modify the system to achieve successful cytokinesis. In this review (which is part of the Cytokinesis series), we discuss the relevant physical properties of cells, how these properties are measured and the basic models that are used to understand cell mechanics. Finally, we present our current understanding of how cytokinesis mechanics work.