State-of-the-art relativistic four-component DFT-GIAO-based calculations of H-1 NMR. chemical shifts of a series of 3d, 4d, and 5d transition-metal hydrides have revealed significant spin-orbit-induced heavy atom effects on the hydride shifts, in particular for several 4d and 5d complexes. The spin-orbit (SO) effects provide substantial, in some cases even the dominant, contributions to the well-known characteristic high-field hydride shifts of complexes with a partially filled d-shell, and thereby augment the Buckingham-Stephens model of off-center paramagnetic ring currents. In contrast, complexes with a 4d(10) and 5d(10) configuration exhibit large deshielding SO effects on their hydride H-1 NMR shifts. The differences between the two classes of complexes are attributed to the dominance of pi-type d-orbitals for the true transition-metal systems compared to sigma-type orbitals for the d(10) systems.