Advances in determination of polymer structure and in preservation of structure for electron microscopy provide the best view to date of how polysaccharides and structural proteins are organized into plant cell walls. The walls that form and partition dividing cells are modified chemically and structurally from the walls expanding to provide a cell with its functional form. In grasses, the chemical structure of the wall differs from that of all other flowering plant species that have been examined. Nevertheless, both types of wall must conform to the same physical laws. Cell expansion occurs via strictly regulated reorientation of each of the wall's components that first permits the wall to stretch in specific directions and then lock into final shape. This review integrates information on the chemical structure of individual polymers with data obtained from new techniques used to probe the arrangement of the polymers within the walls of individual cells. We provide structural models of two distinct types of walls in flowering plants consistent with the physical properties of the wall and its components.