This article provides an overview of the key concepts and recent theoretical developments in computational modeling of complex metal hydrides with a focus on applications in hydrogen storage. Density functional theory based first-principles calculations have played an important role in understanding the structural and thermodynamic properties of these materials. Methods for predicting crystal structures and hydrogen positions in complex hydrides have been developed to complement experimental synthesis and characterization. Together with an efficient formalism for determining multinary phase diagrams under variable temperature and hydrogen pressure (the grand-canonical linear programming method), they constitute a complete first-principles framework for designing new hydrogen storage reactions. We also review the progress in modeling reaction kinetics in a prototypical complex hydride (i.e., a transition metal catalyzed sodium alanate [NaAlH4]). While many aspects of titanium-doped NaAlH4 remain hotly disputed, we discuss areas where satisfactory quantitative understanding has been achieved: diffusive metal mass transport, bulk substitution of Ti, and hydrogen dissociation.