All significant experimental measurements and many theoretical calculation the spectroscopy and structure of the isotopic lithium hydrides (LiH)-L-6, (LiH)-Li-7, (Li-6D), (Li-7D) are identified and reviewed. Published molecular constant determinations from conventional and laser spectroscopy are evaluated; recommended spectroscopic constants for the X 1SIGMA+, A 1SIGMA+ and B 1PI states are tabulated. Potential energy curves (RKR, IPA and hybrid) for the X 1SIGMA+ A 1SIGMA+ and B 1PI states are evaluated and recommended curves are tabulated. Dissociation energy estimates are evaluated and recommended D0 and D(e) values tabulated for the X 1SIGMA+, A 1SIGMA+ and B 1PI states. Accurate electronic structure calculations (Hartree Fock or better) on this ''workbench of theoretical chemistry'' are listed and described briefly; all excited electronic states considered are included. Experimental and theoretical radiative and dipole properties are noted and discussed. Adiabatic corrections to the Born-Oppenheimer approximation are also reviewed. Calculations on LiH+ and LiH- are also listed and described briefly.