We obtain gas-phase homolytic Al–H bond dissociation enthalpies (BDEs) at the CCSD(T)/CBS level for a set of neutral aluminium hydrides (which we refer to as the AlHBDE dataset). The Al–H BDEs in this dataset differ by as much as 79.2 kJ mol−1, with (H2B)2Al–H having the lowest BDE (288.1 kJ mol−1) and (H2N)2Al–H having the largest (367.3 kJ mol−1). These results show that substitution with at least one –AlH2 or –BH2 substituent exerts by far the greatest effect in modifying the Al–H BDEs compared with the BDE of monomeric H2Al–H (354.3 kJ mol−1). To facilitate quantum chemical investigations of large aluminium hydrides, for which the use of rigorous methods such as W2w may not be computationally feasible, we assess the performance of 53 density functional theory (DFT) functionals. We find that the performance of the DFT methods does not strictly improve along the rungs of Jacob’s Ladder. The best-performing methods from each rung of Jacob’s Ladder are (mean absolute deviations are given in parentheses): the GGA B97-D (6.9), the meta-GGA M06-L (2.3), the global hybrid-GGA SOGGA11-X (3.3), the range-separated hybrid-GGA CAM-B3LYP (2.1), the hybrid-meta-GGA ωB97M-V (2.5) and the double-hybrid methods mPW2-PLYP and B2GP-PLYP (4.1 kJ mol−1).