Recent strides have been made in both the modeling and measurement of fluid flow on the nanoscale. Carbon nanotubes, with their atomic dimensions and atomic smoothness, are ideal materials for studying such flows. This Progress Report describes recent modeling and experimental advances concerning fluid transport in carbon nanotubes. The varied flow characteristics predicted by molecular dynamics are described, as are the roles of defects and chirality on transport. Analytical models are increasingly being used to describe nanofluidic transport by relaxing many of the assumptions commonly used to describe bulk water. Recent experimental studies examine the size dependence of flow enhancements through carbon nanotubes and use varied spectroscopies to probe water structure and dynamics in these systems. Carbon nanotubes are finding increasing applications in biology, from protein filters to platforms for cell interrogation.