The present study examines the quality of the restricted Hartree-Fock (RHF) ab initio, B3LYP hybrid density functional theory (DFT), and relativistic zeroth-order regular approximation (ZORA) DFT methods for the calculation of phosphorus chemical shift (CS) tensors in phosphine, phosphido, and phosphinidene transition-metal complexes. A detailed comparison of calculated and experimental P-31 CS tensors allows us to identify the characteristic advantages of each computational method. The results from B3LYP and ZORA-DFT calculations indicate that a double-zeta quality basis set reproduces experimental values of the principal components of the P-31 CS tensor in many of the phosphorus-containing transition-metal complexes investigated, whereas the RHF method requires a triple-zeta doubly polarized basis set, yet fails in the case of the terminal phosphido group. Inclusion of the spin-orbit relativistic correction with the ZORA-DFT formalism requires a triple-zeta quality basis set to reproduce the experimental data. We demonstrate the merit of modern computational methods for investigating theoretically the effect of geometric variations upon the phosphorus CS tensor by systematically altering the W-P bond length and the W-P-C-Me bond angle in W(CO)(5)(PMe3). Additionally, a previously reported correlation, determined experimentally, relating the P-31 CS tensor to the Fe-P-Fe bond angle in a series of iron phosphido-bridging compounds, has been reproduced with calculations using the model compound Fe-2(CO)(6)(mu(2)-PPh2)(mu(2)-Cl). The results presented demonstrate the value of modern computational techniques for obtaining a greater understanding of the relationship between phosphorus chemical shifts and molecular structure.