The NMR properties (chemical shift and spin-spin coupling constants) of (129)Xe in covalent compounds and weakly bound complexes have been investigated by DFT methods including relativistic effects. For covalent species, a good agreement between experimental and calculated results is achieved without scalar relativistic effects, but their inclusion (with a triple-zeta, double-polarization basis set) leads to some improvement in the quality of the correlation. The spin-orbit coupling term has a significant effect on the shielding constant, but makes a small contribution to the chemical shift. Coupling constants contain substantial contributions from the Fermi contact and paramagnetic spin-orbit terms; unlike light nuclei the spin-dipole term is also large, whereas the diamagnetic spin-orbit term is negligible. For van der Waals dimers, the dependence of the xenon chemical shift and anisotropy is calculated as a function of the distance. Small (<1 Hz) but non-negligible through-space coupling constants between (129)Xe and (13)C or (1)H are predicted. Much larger couplings, of the order of few Hz, are calculated between xenon and (17)O in a model silicate residue.