Hydrogen-based fuel cells are promising solutions for the efficient and clean delivery of electricity. Since hydrogen is an energy carrier, a key step for the development of a reliable hydrogen-based technology requires solving the issue of storage and transport of hydrogen. Several proposals based on the design of advanced materials such as metal hydrides and carbon structures have been made to overcome the limitations of the conventional solution of compressing or liquefying hydrogen in tanks. Nevertheless none of these systems are currently offering the required performances in terms of hydrogen storage capacity and control of adsorption/desorption processes. Therefore the problem of hydrogen storage remains so far unsolved and it continues to represent a significant bottleneck to the advancement and proliferation of fuel cell and hydrogen technologies. Recently, however, several studies on graphene, the one-atom-thick membrane of carbon atoms packed in a honeycomb lattice, have highlighted the potentialities of this material for hydrogen storage and raise new hopes for the development of an efficient solid-state hydrogen storage device. Here we review on-going efforts and studies on functionalized and nanostructured graphene for hydrogen storage and suggest possible developments for efficient storage/release of hydrogen under ambient conditions.