Contents Summary 505 I. Introduction 505 II. Models of plant cell division 505 III. Establishing the division plane 506 IV. Maintaining the division plane during mitosis and cytokinesis 509 Acknowledgements 510 References 510 SUMMARY: Plants, a significant source of planet-wide biomass, have an unique type of cell division in which a new cell wall is constructed de novo inside the cell and guided towards the cell edge to complete division. The elegant control over positioning this new cell wall is essential for proper patterning and development. Plant cells, lacking migration, tightly coordinate division orientation and directed expansion to generate organized shapes. Several emerging lines of evidence suggest that the proteins required for division-plane establishment are distinct from those required for division-plane maintenance. We discuss recent shape-based computational models and mutant analyses that raise questions about, and identify unexpected connections between, the roles of well-known proteins and structures during division-plane orientation.