The alanates (complex aluminohydrides) have relatively high gravimetric hydrogen density and are among the most promising solid-state hydrogen-storage materials. In this work, the crystal structure and electronic structure of pure and mixed-alkali alanates were calculated by ground-state density-functional band-structure calculations. The results are in excellent correspondence with available experimental data. The properties of the pure alanates were compared, and the relatively high stability of the Li3AlH6 phase was pointed out as an important difference that may explain the difficulty of hydrogenating lithium alanate. The alkali alanates are nonmetallic with calculated band gaps around 5 eV and 2.5–3 eV for the tetra- and hexahydrides. The bonding was identified as ionic between the alkali cations and the aluminohydride complexes, while it is polar covalent within the complex. A broad range of hypothetical mixed-alkali alanate compounds was simulated, and four were found to be stable compared to the pure alanates and each other: LiNa2AlH6, K2LiAlH6, K2NaAlH6, and K2.5Na0.5AlH6. No mixed-alkali tetrahydrides were found to be stable, and this was explained by the local coordination within the different compounds. The only alkali alanate that seemed to be close to fulfilling the international hydrogen density targets was NaAlH4.