The primary architecture of the aerial part of plants is controlled by the shoot apical meristem, a specialized tissue containing a stem cell niche. The iterative generation of new aerial organs, (leaves, lateral inflorescences and flowers) at the meristem follows regular patterns, called phyllotaxis. Phyllotaxis has long been proposed to self-­‐organize from the combined action of growth and of inhibitory fields blocking organogenesis in the vicinity of existing organs in the meristem. In this review we will highlight how a combination of mathematical/computational modeling and experimental biology has demonstrated that the spatio-­‐temporal distribution of the plant hormone auxin controls both organogenesis and the establishment of inhibitory fields. We will discuss recent advances showing that auxin likely acts through a combination of biochemical and mechanical regulatory mechanisms that control not only the pattern of organogenesis in the meristem but also post-­‐meristematic growth, to shape the shoot.