Boundary-layer theory is crucial in understanding why certain phenomena
occur. We start by reviewing steady and unsteady separation from
the viewpoint of classical non-interactive boundary-layer theory. Next,
interactive boundary-layer theory is introduced in the context of unsteady
separation. This discussion leads onto a consideration of large-
Reynolds-number asymptotic instability theory. We emphasise that a
key aspect of boundary-layer theory is the development of singularities
in solutions of the governing equations. This feature, when combined
with the pervasiveness of instabilities, often forces smaller and smaller
scales to be considered. Such a cascade of scales can limit the quantitative
usefulness of solutions. We also note that classical boundarylayer
theory may not always be the large-Reynolds-number limit of the
Navier-Stokes equations. This is because of the possible amplication of
short-scale modes, which are initially exponentially small, by a Rayleigh
instability mechanism.