Organisms as diverse as bacteria, fungi, plants, and animals manifest a property called "polarity." The literature shows that polarity emerges as a consequence of different mechanisms in different lineages. However, across all unicellular and multicellular organisms, polarity is evident when cells, organs, or organisms manifest one or more of the following: orientation, axiation, and asymmetry. Here, we review the relationships among these three features in the context of cell division and the evolution of multicellular polarity primarily in plants (defined here to include the algae). Data from unicellular and unbranched filamentous organisms (e.g., Chlamydomonas and Ulothrix) show that cell orientation and axiation are marked by cytoplasmic asymmetries. Branched filamentous organisms (e.g., Cladophora and moss protonema) require an orthogonal reorientation of axiation, or a localized cell asymmetry (e.g., "tip" growth in pollen tubes and fungal hyphae). The evolution of complex multicellular meristematic polarity required a third reorientation of axiation. These transitions show that polarity and the orientation of the future plane(s) of cell division are dyadic dynamical patterning modules that were critical for multicellular eukaryotic organisms.