During cytokinesis, animal and fungal cells form a membrane furrow via actomyosin ring constriction. Our understanding of actomyosin ring-driven cytokinesis stems extensively from the fission yeast model system. However, unlike animal cells, actomyosin ring constriction occurs simultaneously with septum formation in fungi. While the formation of an actomyosin ring is essential for cytokinesis in fission yeast, proper furrow formation also requires septum deposition. The molecular mechanisms of spatiotemporal coordination of septum deposition with actomyosin ring constriction are poorly understood. Although the role of the actomyosin ring as a mechanical structure driving furrow formation is better understood, its role as a spatiotemporal landmark for septum deposition is not widely discussed. Here we review and discuss the recent advances describing how the actomyosin ring spatiotemporally regulates membrane traffic to promote septum-driven cytokinesis in fission yeast. Finally, we explore emerging questions in cytokinesis, and discuss the role of extracellular matrix during cytokinesis in other organisms.