Cytokinesis partitions the cytoplasm of a dividing cell. Unlike yeast and animal cells, which form cleavage furrows from the plasma membrane, cells in higher plants make a new membrane independently of the plasma membrane by homotypic fusion of vesicles. In somatic cells, a plant-specific cytoskeletal array, called a phragmoplast, is thought to deliver vesicles to the plane of division. Vesicle fusion generates a membranous network, the cell plate, which, by fusion of later-arriving vesicles with its margin, expands towards the cell periphery and eventually fuses with the plasma membrane. In this review (part of the Cytokinesis series), I describe recent studies addressing the mechanisms that underlie cell-plate formation and the coordinated dynamics of membrane fusion and cytoskeletal reorganization during progression through cytokinesis.