Hydrogen economy towards the utilization of hydrogen as a clean and sustainable energy source has three ingredients. These are (i) hydrogen production; (ii) hydrogen storage; and (iii) fuel cells. Optimization of fuel cells for desired applications is a challenging engineering problem. The subject matter of my thesis is to develop nanostructures and to reveal physical and chemical mechanisms for the production of free hydrogen and its high capacity storage. The predictions of this study are obtained from rst-principles density functional theory and nite temperature molecular dynamics calculations, phonon calculations and transition state analyses. Recent studies have revealed that single layer transition metal oxides and dichalcogenides (MX2; M:Transition metal, X:Chalcogen atom) may o er properties, which can be superior to those of graphene. Synthesis of single layer free standing MoS2 and its nanoribbons, fabrication of transistor using this nanostructure, active edges of akes of MoS2 taking a part in hydrogen evolution reaction (HER) boost the interest in these materials. The electronic, magnetic, mechanical, elastic and vibrational properties of three-, two- and quasi one-dimensional MoS2 are investigated. Dimensionality e ects such as indirect to direct band gap transition, shift of phonon modes upon three- to two- dimensional transition, half metallic nanoribbons are revealed. Functionalization of single layer MoS2 and its nanoribbons are achieved by creating vacancy defects and adatom adsorption. Moreover, out of 88 di erent combinations of MX2 compounds (transition metal dichalcogenides) it is also predicted that more than 50 single layer, free standing MX2 can be stable in honeycomb like structures and o er novel physical and chemical properties relevant for hydrogen economy. It is predicted that H2O can be split spontaneously into its constituents O and H at speci c vacancy defects of single layer MoS2 honeycomb structure. Interacting with the photons of visible light, H atoms adsorbed to two folded S atoms surrounding the vacancy start to migrate and eventually form free H2 molecules, which in turn, are released from the surface. Not only taking a part in HER, but also it is shown that MoS2 as a catalyst can release H2 molecule from water. Also other possible candidates among the manifold of stable MX2 compounds, which are capable of presenting similar catalytic activities are deduced. In an e ort to obtain a high capacity hydrogen storage medium, the functionalization of graphene with adatoms is investigated. It is found that Li-graphene complex can serve as a high capacity hydrogen storage medium. A gravimetric storage capacity of 12.8 wt % is attained, whereby each Li atom donates the significant part of its charge to graphene and eventually attracts up to four H2 through a weak interaction. Similarly Ca adatoms can hold H2 molecule on graphene up to 8.4 wt % through an interesting mechanism involving charge exchange among Ca, graphene and H2.