A theory is presented in which much of the structure of spiral galaxies arises from a percolation phase transition that underlies the phenomenon of propagating star formation. According to this view, the appearance of spiral arms is a consequence of the differential rotation of the galaxy and the characteristic divergence of correlation lengths for continuous phase transitions. Other structural properties of spiral galaxies, such as the distribution of the gaseous components and the luminosity, arise directly from a feedback mechanism that pins the star formation rate close to the critical point of the phase transition. The approach taken in this article differs from traditional dynamical views. The argument is presented that, at least for some galaxies, morphological and other features are already fixed by general properties of phase transitions, irrespective of detailed dynamic or other considerations.