The energy arteries of the corporate body of mankind are still fed mainly by fossil fuels; but they are in danger of running dry soon unless new energy sources are made available. One of the most important as well as the most ecologically pure power source is hydrogen, that constitutes the heart of hydrogen power engineering and considered as a future alternative to fossil power sources. The chemistry of carbon nanomaterials and hydrogen materials science will play an important role in hastening the conversion to the Hydrogen Energy System. In this connection the research and application of materials capable of interacting actively with hydrogen, its accumulating and storing will be of the utmost significance. This is of particular actuality for creation of mobile energy sources both for mobile telephones and for hybrid electric cars that are developed by all large car manufacturers of the world. In this connection the hydrogen capacity of carbon nanostructural materials, such as fullerenes, nanotubes, nanofibers and other nanostructures, has aroused a special interest of researchers. Hydriding metals, alloys, nanocarbon and composite materials can store hydrogen safely at relatively low pressures and temperatures. Very many other applications are also possible - such as heating and cooling, waste heat storage, pumping, pressurizing, heat-pumping, hydrogen purifying, deuterium separation, electricity production, etc. As a source of 'clean' energy, hydrogen is also going to be the permanent answer to another global problem caused by utilization of fossil fuels, such as the greenhouse effect, climate change, acid rains, ozone layer depletion, pollution and oil spills.