For decades after the discovery that a contractile ring made of actin filaments and myosin II produces the force to constrict the cleavage furrow of animal cells, the complexity of cytokinesis has slowed progress in understanding the mechanism. Mechanistic insights, however, have been obtained by genetic, biochemical, microscopic and mathematical modelling approaches in the fission yeast Schizosaccharomyces pombe. Many features that have been identified in fission yeast are probably shared with animal cells, as both inherited many cytokinesis genes from their common ancestor about one billion years ago.