Low dimensional materials are those that possess at least one physical boundary small enough to confine the electrons or phonons. This quantum confinement reduces the dimensionality of the material and imparts unique and novel properties that are not seen in their bulk forms. Examples include quantum dots (0-D), carbon nanotubes (1-D), and graphene (2-D). Accordingly, these materials exhibit new concepts in mass and energy transport that can be exploited for technological applications. In this Perspective, we review several topics related to mass and energy transport in and around carbon-based low dimensional materials. Recent developments in the study of matter being transported through carbon nanotube and graphene nanopores are reviewed, as well as applications of excitonic, thermal, and electronic energy transport in carbon nanotubes. The nanometer-scale interior of a single-walled carbon nanotube (SWCNT) has been studied as a unique nanopore, exhibiting periodic ionic conduction currents and dimensionally confined material phases. The mechanism of gas transport through atomic-scale holes in graphene, which is otherwise a perfect barrier material, has been analytically studied. These insights on nanoscale mass transport will have important implications in systems ranging from biological nanopores to advanced water filtration devices. The electronic structure of semiconducting SWCNTs allows photogenerated excitons to be harnessed for single-molecule biosensing and as elements of a new class of all-nanocarbon near-infrared photovoltaics. The extremely high thermal and electrical conductivities of carbon nanotubes allows the generation of electrical energy from chemical reactions. The understanding of how low dimensional physics and chemistry influences mass and energy transport will facilitate the application of these materials to a variety of scientific challenges.