In animal cells, cytokinesis requires the formation of a cleavage furrow that divides the cell into two daughter cells. Furrow formation is achieved by constriction of an actomyosin ring that invaginates the plasma membrane. However, fungal cells contain a rigid extracellular cell wall surrounding the plasma membrane; thus, fungal cytokinesis also requires the formation of a special septum wall structure between the dividing cells. The septum biosynthesis must be strictly coordinated with the deposition of new plasma membrane material and actomyosin ring closure and must occur in such a way that no breach in the cell wall occurs at any time. Because of the high turgor pressure in the fungal cell, even a minor local defect might lead to cell lysis and death. Here we review our knowledge of the septum structure in the fission yeast Schizosaccharomyces pombe and of the recent advances in our understanding of the relationship between septum biosynthesis and actomyosin ring constriction and how the two collaborate to build a cross-walled septum able to support the high turgor pressure of the cell. In addition, we discuss the importance of the septum biosynthesis for the steady ingression of the cleavage furrow.