Plant cytokinesis is orchestrated by a specialized structure, the phragmoplast. The phragmoplast first occurred in representatives of Charophyte algae and then became the main division apparatus in land plants. Major cellular activities, including cytoskeletal dynamics, vesicle trafficking, membrane assembly, and cell wall biosynthesis, cooperate in the phragmoplast under the guidance of a complex signaling network. Furthermore, the phragmoplast combines plant-specific features with the conserved cytokinetic processes of animals, fungi, and protists. As such, the phragmoplast represents a useful system for understanding both plant cell dynamics and the evolution of cytokinesis. We recognize that future research and knowledge transfer into other fields would benefit from standardized terminology. Here, we propose such a lexicon of terminology for specific structures and processes associated with plant cytokinesis.