Carbon materials exist in a large number of allotropic forms and exhibit a wide range of physical and chemical properties. From the perspective of fluidics, particularly within the confines of the nanoscale afforded by one-dimensional carbon nanotubes (CNTs) and two-dimensional graphene structures, many unique properties have been discovered. However, other questions, such as the link between electronic states and hydrodynamics and accurate model predictions of transport, remain unanswered. Theoretical studies, experiments in large-scale ensembles of CNTs and stacked graphene sheets, and precise measurements at the single-pore and single-molecule level have helped in our understanding. These activities have led to explosive growth in the field, now known as carbon nanofluidics. The ability to produce membranes and devices from fluid phases of graphene oxide, which retain these special properties in molecular-scale flow channels, promises realization of applications in the near term.