A study of the LinHn and Lin+1Hn+ clusters with n up to 7 and Li14H13+ using both density-functional theory (DFT) and a model potential is presented. The combined use of these two methods has shown great efficiency. It has enabled us to perform exhaustive explorations of the potential energy surfaces and to study a large number of isomers. Our results show that the structures of the Li-H clusters are very close to typical ionic structures and that the Li-H bond is almost totally ionic. Moreover, the stability of the small clusters is not directly related to the number of ionic bonds formed, and families of structures exist throughout the sizes studied. Our study has also shown that a very simple ionic model potential yields good starting structures and not unreasonable energies. This simple model, however, exhibits two problems: The number of minima in the potential is too large compared to DFT. and its accuracy is by far insufficient to enable one to interpret experimental results. Finally, a good agreement is observed between B3LYP results and the available experimental data.