This paper is an introduction to the astronomical material underlying the Varenna Symposium on Aerodynamical Phenomena in Stellar Atmospheres. The term « aerodynamical phenomena » rather than simply « velocity fields » is used in the title of the symposium to imply that primary concern centers as much on the physical phenomena and consequences associated with the presence of velocity fields as it does simply on the velocity fields themselves. To fully appreciate this distinction between aerodynamical phenomena and velocity fields from the astronomer's viewpoint, one must consider it against the background of the classical theory (*) of stellar atmospheres, which assumes that all the properties of the atmosphere are strictly controlled by the radiation field. The thermodynamic state of the classical atmosphere is fixed by the three conditions of radiative equilibrium (no energy transport other than by radiation), hydrostatic equilibrium (no mechanical momentum transport), and local thermodynamic equilibrium at a temperature fixed by the local energy-density of the radiation field (complete coupling between radiation field and atomic degrees of freedom). Analyses of stellar spectra under the framework of this classical atmospheric model take account of the presence of velocity fields (other than thermal) only in their effect upon the atomic absorption coefficient, not in their energetic or momentum coupling to the thermodynamic state of the atmosphere. Thus, if we become interested in aerodynamic phenomena in stellar atmospheres, we must investigate the possible perturbation these velocity fields may have upon the thermodynamic state of the atmosphere. We develop a primary concern with differential motions, velocity gradients, and dissipation mechanisms — all quantities which may produce a local non-relative energy source — rather than directing our attention only at stellar rotation and uniform expansion of an atmosphere. Thus, what we call aerodynamic phenomena embraces not only velocity fields but also their influence upon the thermodynamic state of the atmosphere.