The phonons and the crystal structure of the complex hydride LiBH4 are studied on single crystals using micro-Raman spectroscopy. The symmetry of the modes is determined by polarization-dependent measurements at liquid helium temperature, allowing a better comparison and a more reliable assignment to the computed phonon wavenumbers. This has led to the revision of some former assignments made from Raman measurements on polycrystalline samples. In addition, a higher integration time allowed the detection of very weak lines, so that 35 out of 36 predicted Raman lines have been identified. We have also performed explorative Raman measurements on Mg(BH4)2 powders. In contrast to LiBH4, the very poor crystallinity of this material inhibits the exploitation of the full potential of Raman spectroscopy. Only broad lines are observed, which we compare to phonon wavenumbers calculated for various possible structures using density functional theory. Copyright © 2011 John Wiley & Sons, Ltd.