The structure of the quiet solar corona is considered, excluding the effect of magnetic active regions. Starting with a simple one-dimensional geometry, models are derived both from ab initio theory and from analysis of spectral line intensities. To overcome the inconsistencies which arise, account is taken progressively of two-dimensional effects; the concentration of magnetic fields at the supergranule cell boundaries and the effect of coronal holes. The relationship is discussed between coronal holes, solar wind onset, the observation of fast streams, and the implication for other stars. The transition region is shown to be thicker than often assumed, thereby allowing the neglect of some of the more sophisticated non-Maxwellian effects which have been proposed in the past.