We review recent progress in the transport of a fluid phase through spaces of simple geometry (parallel sided slits or cylinders) in which the confining walls restrict the fluid phase to a few molecular widths in at least one dimension. We emphasise the fact that in such spaces, the contingent solid phase plays a major role in creating strong non-uniformity in directions normal to the confining surface, even at very low fluid densities and ambient temperatures. Furthermore, the adsorbent field of the solid distorts molecular trajectories from linear and is a major factor in determining the extent to which momentum tangential to the surface is re-allocated in the collision process. The first part of the review surveys briefly the contributions that can be made from computer simulation, and the nature of some theoretical constructs relating to the problem; we focus, in particular on the theoretical advances that have been made in Queensland over the last few years. Following this we turn attention to progress in understanding the molecular scattering process at the point of normal momentum reversal at the surface and the theoretical and experimental developments relating to the intriguing possibility of 'superfast' flow in carbon nanotubes.