During the last decades hydrogen has attracted worldwide attention as an energy carrier. MgH2 is one of the most promising materials for hydrogen storage due to its high hydrogen uptake, large reserves and low cost. However, the potential for practical use of MgH2 is severely limited because of its high temperature of hydrogen discharge, slow desorption kinetics and a high reactivity toward air and oxygen. Nevertheless, the transition metals doping of Mg greatly enhances the kinetics of hydrogen uptake and release and in particular cases decreases its stability. Despite a huge number of experimental studies fundamental aspects of these phenomena remain unclear. Theoretical researches could provide an insight in metal-hydrogen bonding that governs both the thermodynamic stability and the hydrogen sorption kinetics. In this paper a brief review of the recent theoretical works concerning the influence of transition metals on the electronic structure and stability of magnesium hydride MgH2 is given.