Hydrogen is the cleanest, sustainable and renewable energy carrier, and a hydrogen energy system is expected to progressively replace the existing fossil fuels in the future, the latter are being depleted very fast and causes severe environmental problems. In particular, one potential use of hydrogen lies in powering zero-emission vehicles via a proton exchange membrane fuel cell to reduce atmosphere pollution. To achieve this goal feasible onboard hydrogen storage systems have to be developed. The recent discovery of the high and reversible hydrogen storage capacity of carbon nanotubes makes such a system very promising. In this overview, theoretical predictions and experimental results on the hydrogen uptake of carbon nanotubes and nanofibers are summarized, and we point out that, in order to accelerate the development of carbon nanotubes and nanofibers as a practical hydrogen storage medium in fuel cell-driven vehicles, many efforts have to be made to reproduce and verify the results both theoretically and experimentally, and to investigate their volumetric capacity, cycling characteristics and release behavior.