All significant experimental measurements and theoretical calculations of the spectroscopy and structure of the alkali hydrides NaH, KH, RbH, and CsH, and the corresponding alkali deuterides, are identified and reviewed. Published molecular constant determinations from conventional and laser spectroscopy are evaluated; recommended spectroscopic constants forX 1&Sgr;+andA 1&Sgr;+states are tabulated. RKR and hybrid potential energy curves are evaluated; recommended RKR curves forX 1&Sgr;+andA 1&Sgr;+states are tabulated. Ground state dissociation energy (De) estimates are evaluated; recommendedX 1&Sgr;+andA 1&Sgr;+stateDeandD0values are tabulated. Accurate electronic structure calculations (Hartree–Fock or better) are listed and described briefly; all excited electron states considered are included. Experimental and theoretical radiative and dipole properties are noted and discussed. Calculations on the positive and negative ions of the four diatomic alkali hydrides are also listed and described briefly.