Cytokinesis, the final stage of the cell division cycle, requires the proper placement, assembly and contraction of an actomyosin-based contractile ring. Conserved sets of cytokinesis proteins and pathways have now been identified and characterized functionally. Additionally, fluorescent protein fusion technology enables quantitative high-resolution imaging of protein dynamics in living cells. For these reasons, the study of cytokinesis is now ripe for quantitative, systems-level approaches. Here, we review our current understanding of the molecular mechanisms of contractile ring dynamics in the model organism Schizosaccharomyces pombe (fission yeast), focusing on recent examples that illustrate a synergistic integration of quantitative experimental data with computational modeling. A picture of a highly dynamic and integrated system consisting of overlapping networks is beginning to emerge, the detailed nature of which remains to be elucidated.