In this review, attention will be focussed exclusively on the winds of hot stars, concentrating for the most part on spectral types 0 and B. For these stars, a clear consensus has emerged that it is the gradient of selective radiation pressure - i.e., line-driving - that explains the high terminal velocities, typically ~ 2000 km s−1, of their winds. Accordingly, few would now doubt that the supersonic zones of these winds present us with rather clean examples of line-driven flow, whose investigation therefore properly belongs under the heading “Radiation Hydrodynamics”. Moreover, in marked contrast with other astronomical environments where line-driven winds may exist, the stellar case is geometrically and parametrically well defined and is thus by far the best natural example from which to learn about such flows.