The mechanism underlying cytokinesis, the final step in cell division, remains one of the major unsolved questions in basic cell biology. Thanks to advances in functional genomics and proteomics, we are now able to assemble a "parts list" of proteins involved in cytokinesis. In this review, we discuss how to relate this parts list to biological mechanism. For easier analysis, we split cytokinesis into discrete steps: cleavage plane specification, rearrangement of microtubule structures, contractile ring assembly, ring ingression, and completion. We report on the advances that have been made to understand these steps and how they can be integrated into a global understanding of cytokinesis. We also discuss the extent to which classic questions have been answered and identify major outstanding questions.