Dividing animal and plant cells maintain a constant chromosome content through temporally separated rounds of replication and segregation. Until recently, the mechanisms by which animal and plant cells maintain a constant surface area have been considered to be distinct. The prevailing view was that surface area was maintained in dividing animal cells through temporally separated rounds of membrane expansion and membrane invagination. The latter event, known as cytokinesis, produces two physically distinct daughter cells and has been thought to be primarily driven by actomyosin-based constriction. By contrast, membrane addition seems to be the primary mechanism that drives cytokinesis in plants and, thus, the two events are linked mechanistically and temporally. In this article (which is part of the Cytokinesis series), we discuss recent studies of a variety of organisms that have made a convincing case for membrane trafficking at the cleavage furrow being a key component of both animal and plant cytokinesis.