Cytokinesis partitions the cytoplasm between two or more nuclei. In higher plants, cytokinesis is initiated by cytoskeleton-assisted targeted delivery of membrane vesicles to the plane of cell division, followed by local membrane fusion to generate tubulo-vesicular networks. This initial phase of cytokinesis is essentially the same in diverse modes of plant cytokinesis whereas the subsequent transformation of the tubulo-vesicular networks into the partitioning membrane may be different between systems. This review focuses on membrane and cytoskeleton dynamics in cell plate formation and expansion during somatic cytokinesis.