Relativistic density functional theory calculations, both with and without the effects of spin-orbitcoupling, have been employed to model hydride NMR chemical shifts for a series of[Ru(NHC)4(L)H]0/+ species (NHC = N-heterocyclic carbene; L = vacant, H2, N2, CO, MeCN, O2, P4,SO2, H-, F- and Cl-), as well as selected phosphine analogues [Ru(R2PCH2CH2PR2)(L)H]+ (R = iPr, Cy;L = vacant, O2). Inclusion of spin-orbit coupling provides good agreement with the experimental data.For the NHC systems large variations in hydride chemical shift are shown to arise from theparamagnetic term, with high net shielding (L = vacant, Cl-, F-) being reinforced by the contributionfrom spin-orbit coupling. Natural chemical shift analysis highlights the major orbital contributions tothe paramagnetic term and rationalizes trends via changes in the energies of the occupied Ru dπorbitals and the unoccupied σ*Ru-H orbital. In [Ru(NHC)4(η2-O2)H]+ a δ-interaction with the O2 ligandresults in a low-lying LUMO of dπ character. As a result this orbital can no longer contribute to theparamagnetic shielding, but instead provides additional deshielding via overlap with the remaining(occupied) dπ orbital under the Lz angular momentum operator. These two effects account for theunusual hydride chemical shift of +4.8 ppm observed experimentally for this species. Calculationsreproduce hydride chemical shift data observed for [Ru(iPr2PCH2CH2PiPr2)2(η2-O2)H]+ (δ = -6.2 ppm)and [Ru(R2PCH2CH2PR2)2H]+ (ca. -32 ppm, R = iPr, Cy). For the latter, the presence of a weak agosticinteraction trans to the hydride ligand is significant, as in its absence (R = Me) calculations predict achemical shift of -41 ppm, similar to the [Ru(NHC)4H]+ analogues. Depending on the strength of theagostic interaction a variation of up to 18 ppm in hydride chemical shift is possible and this factor (thatis not necessarily readily detected experimentally) can aid in the interpretation of hydride chemicalshift data for nominally unsaturated hydride-containing species. The synthesis and crystallographiccharacterization of the BArF4- salts of [Ru(IMe4)4(L)H]+ (IMe4 = 1,3,4,5-tetramethylimidazol-2-ylidene; L = P4, SO2; ArF = 3,5-(CF3)2C6H3) and [Ru(IMe4)4(Cl)H] are also reported.