Pressure-induced structural, electronic, and thermodynamic changes in $\alpha \text{−}\mathrm{Al}{H}_3$ were investigated using synchrotron x-ray powder diffraction and density-functional theory. No first-order structural transitions were observed up to $7\mathrm{GPa}$. However, increasing Bragg peak asymmetry with pressure suggests a possible monoclinic distortion at moderate pressures $(1–7\mathrm{GPa})$. The pressure-volume relationship was fit to the Birch-Murnaghan equation of state to give a bulk modulus of approximately $40\mathrm{GPa}$. The reduced cell volume at high pressure is accommodated by octahedral tilting and a decrease of the Al-H bond distance. Ab initio calculations of the free energy indicate that hydrogenation becomes favorable at $H_2$ pressures above $0.7\mathrm{GPa}$ at $300K$. Electronic density of states calculations reveal a slight decrease in the band gap with pressure but no evidence of an insulator-to-metal transition predicted by previous high-pressure studies. Calculated Mulliken charges and bond populations suggest a mixed ionic and covalent Al-H bond at $1\mathrm{atm}$ with an increase in covalent character with pressure.