The great complexity and plasticity of aerial plant shapes largely results from the activity of the shoot apical meristem (SAM), a group of undifferentiated cells which produces all the aboveground organs of the plant. Organogenesis at the SAM is regulated by the hormone auxin, which, through an integration of active transport, signalling and transcriptional regulation, determines the positional and temporal information dictating where, when, and how a new organ will be formed. At the cellular level, the information stemming from the regulatory molecular networks influences the growth of the cells within the tissue to give rise to the final organ shape. The growth of plant cells is mainly controlled by the cell wall, a rigid structure mainly made of polysaccharides, which surrounds the cells and links them together in an organismal continuum. Over the years, several lines of evidence have pointed at a role for the regulation of the elasticity of the cell wall, downstream of auxin action, in the formation of organs at the SAM. We have recently shown that auxin also induces a shift toward isotropic growth by modulating the organization of cortical microtubules in peripheral SAM cells, which promotes organ formation. Here, we discuss our results and identify new hypotheses to drive future research.