HYDROGEN IS AN IDEAL FUEL BECAUSE OF ITS ZERO OR LOW POLLUTANT EMISSION DURING COMBUSTION. FOR THE UTILIZATION FOR HYDROGEN, HYDROGEN STORAGE TECHNOLOGY IS NECESSARY, IN WHICH LIGHT, ENVIRONMENTALLY FRIENDLY AND CHEAP MATERIALS ARE REQUIRED TO BE USED SPECIALLY IN THE FUEL CELL VEHICLES. THERE ARE DIFFERENT TECHNIQUES TO STORE HYDROGEN. ALL THOSE TECHNIQUES HAVE TO MEET THE PROVISIONAL DEPARTMENT OF ENERGY OF THE UNITED STATES (DOE) CRITERION. THE DOE HAS ESTABLISHED DIFFERENT TARGETS FOR ON-BOARD HYDROGEN STORAGE SYSTEMS, INCLUDING THE MINIMUM “GRAVIMETRIC” AND “VOLUMETRIC” CAPACITY AND THE REVERSIBILITY OF CHARGING/DISCHARGING PROCESSES. SINCE 1997, WHEN DILLON ET AL. REPORTED THAT THE CARBON NANOTUBES (CNTS) CAN STORE HYDROGEN, NUMEROUS EXPERIMENTAL AND THEORETICAL WORKS HAVE BEEN PERFORMED IN ORDER TO INVESTIGATE HYDROGEN ADSORPTION IN CNTS AND TO IMPROVE THE STORAGE CAPACITY OF THE TUBES BY DOPING THEM. THE CARBON NANOTUBES SEEM TO BE AN ULTIMATE MATERIAL FOR HYDROGEN STORAGE, DUE TO THEIR CHEMICAL STABILITY, LARGE SURFACE AREA, HOLLOWNESS, AND LIGHT MASS. PHYSICAL ADSORPTION IS GENERALLY ACCOUNTED FOR THE WAY THAT HYDROGEN IS STORED IN CARBON MATERIALS AND MOST STUDIES CONCERNING HYDROGEN STORAGE HAVE BEEN CARRIED OUT AT HIGH PRESSURES (1-16MPA) AND LOW TEMPERATURES (80-133K) IN ORDER TO STORE MOLECULAR HYDROGEN BY PHYSISORPTION. HYDROGEN ATOMS CAN BE STORED DOMINANTLY THROUGH THE TUBE WALL BY BREAKING C-C MID BOND, WHILE PRESERVING THE WALL STABILITY OF A NANOTUBE AFTER COMPLETE HYDROGEN INSERTION, RATHER THAN BY THE CAPILLARITY EFFECT THROUGH ENDS OF NANOTUBES. IN THE HYDROGEN EXTRACTION PROCESSES, HYDROGEN MOLECULES IN THE CAPILLARY OF NANOTUBES FIRST DISSOCIATES AND ADSORBS ON TO THE INNER WALL AND IS FURTHER EXTRACTED TO THE OUTER WALL BY THE FLIP-OUT MECHANISM. HYDROGEN STORAGE CAPACITY OF CARBON NANOTUBES AND CARBON NANO FIBERS IS DETERMINED BY PHYSICAL PROPERTIES SUCH AS PORE GEOMETRY, SURFACE AREA, AND APPEARANCE OF GRAPHITE SHEETS. IN THIS PAPER WE DISCUSS ABOUT THE STRUCTURE OF CARBON NANO FIBERS AND CARBON NANOTUBES, AND WE ALSO DISCUSS ABOUT THE HYDROGEN STORAGE ON THESE CARBON NANOMATERIAL’S WHICH USED IN THE ON-BOARD STORAGE OF HYDROGEN IN THE FUEL CELL VEHICLES.