Electronic structure, volume optimization, bulk moduli, elastic constants, and frequencies of the transversal optical vibrations in LiH, NaH, KH, RbH, and CsH are calculated using the full potential augmented plane wave method, extended with local orbitals, and the full potential linearized augmented plane wave method. The obtained results show some common features in the electronic structure of these compounds, but also clear differences, which cannot be explained using simple empirical trends. The differences are particularly prominent in the electronic distributions and interactions in various crystallographic planes. In the light of these findings we have elaborated some selected experimental results and discussed several theoretical approaches frequently used for the description of various alkali hydride properties.