Underlying the architectural complexity of plants are diverse cell types that, under the microscope, easily reveal relationships between cell structure and specialized functions. Much less obvious are the mechanisms by which the cellular growth machinery and mechanical properties of the cell interact to dictate cell shape. The recent combined use of mutants, genomic analyses, sophisticated spectroscopies, and live cell imaging is providing new insight into how cytoskeletal systems and cell wall biosynthetic activities are integrated during morphogenesis. The purpose of this review is to discuss the unique geometric properties and physical processes that regulate plant cell expansion, then to overlay on this mechanical system some of the recent discoveries about the protein machines and cellular polymers that regulate cell shape. In the end, we hope to make clear that there are many interesting opportunities to develop testable mathematical models that improve our understanding of how subcellular structures, protein motors, and extracellular polymers can exert effects at spatial scales that span cells, tissues, and organs.