Aluminum hydride (AlH₃) is a binary metal hydride with a mass hydrogen density of more than 10% and bulk hydrogen density of 148 $\mathrm{kg}{\mathrm{H}}_2/{\mathrm{m}}^3$. Pure aluminum hydride can easily release hydrogen when heated. Due to the high hydrogen density and low decomposition temperature, aluminum hydride has become one of the most promising hydrogen storage media for wide applications, including fuel cell, reducing agents, and rocket fuel additive. Compared with aluminum powder, AlH₃ has a higher energy density, which can significantly reduce the ignition temperature and produce H₂ fuel in the combustion process, thus reducing the relative mass of combustion products. In this paper, the research progress about the structure, synthesis, and stability of aluminum hydride in recent decades is reviewed. We also put forward the challenges for application of AlH₃ and outlook the possible opportunity for AlH₃ in the future.