Abstract In this thesis, the classic Kurland-McGarvey theory for the nuclear magnetic resonance (NMR) chemical shift is presented in a modern framework for paramagnetic systems containing one or more unpaired electrons. First-principles computations are carried out for the NMR shielding tensors in paramagnetic transition-metal complexes. A combined ab initio/density-functional theory (DFT) approach is applied to obtain the necessary electron paramagnetic resonance (EPR) property tensors, i.e., the g-tensor, zero-field splitting tensor (D) and hyperfine coupling tensors (A). In DFT, both the generalised-gradient approximation and hybrid DFT are applied to calculate A. The complete active space self-consistent field theory (CASSCF) and N-electron valence-state perturbation theory (NEVPT2) are applied to calculate the g- and D-tensors. Scalar relativistic effects are included at the second-order Douglas-Kroll-Hess level for the g- and D-tensors and, for A, at the fully relativistic four-component matrix-Dirac-Kohn-Sham level. This methodology is applied to study ¹³C and ¹H chemical shifts and shielding anisotropies in a series of Co(II) pyrazolylborate complexes, a Cr(III) quinolyl-functionalised cyclopentadienyl complex, Ni(II) acetylacetonate complexes and various metallocenes. The results obtained from these calculations are generally in a good agreement with the experimental data, in some cases, for Ni(II) complexes, allowing to correct the experimental spectral signal assignment. CASSCF/NEVPT2 computations (especially for the D-tensor) are more accurate than DFT, which is useful for the purpose of obtaining the NMR chemical shifts. The computational results obtained are dependent on the choice of molecular geometry (experimental X-ray or computationally optimised), wavefunction used for g and D (CASSCF or NEVPT2), DFT functional for A, and the quality of the basis sets. The locally dense basis method used for the CASSCF/NEVPT2 computations is less expensive and gives equally good results for g and D as fully balanced basis sets. The scalar relativistic influences are usually small for g and D, but are large for A. Due to that, scalar relativistic effects are important for the chemical shift and shielding anisotropy, especially for carbon nuclei. These first-principles computations based on combined ab initio/DFT methodology are promising for the treatment of important electron correlation and scalar relativistic effects in the calculation of pNMR chemical shifts and shielding anisotropies. This work provides a straightforward platform for further development of pNMR shielding theory in terms of first-principles wavefunctions, as well as for applications in current problems in bio- and materials sciences, including low-temperature experiments. / Original papers The original papers are not included in the electronic version of the dissertation. Vaara, J., Rouf, S. A., & Mareš, J. (2015). Magnetic Couplings in the Chemical Shift of Paramagnetic NMR. Journal of Chemical Theory and Computation, 11(10), 4840–4849. https://doi.org/10.1021/acs.jctc.5b00656 Rouf, S. A., Mareš, J., & Vaara, J. (2015). ¹H Chemical Shifts in Paramagnetic Co(II) Pyrazolylborate Complexes: A First-Principles Study. Journal of Chemical Theory and Computation, 11(4), 1683–1691. https://doi.org/10.1021/acs.jctc.5b00193 Rouf, S. A., Jakobsen, V. B., Mareš, J., Jensen, N. D., McKenzie, C. J., Vaara, J., & Nielsen, U. G. (2017). Assignment of solid-state ¹³C and ¹H NMR spectra of paramagnetic Ni(II) acetylacetonate complexes aided by first-principles computations. Solid State Nuclear Magnetic Resonance, 87, 29–37. https://doi.org/10.1016/j.ssnmr.2017.07.003 Rouf, S. A., Mareš, J., & Vaara, J. (2017). Relativistic Approximations to Paramagnetic NMR Chemical Shift and Shielding Anisotropy in Transition Metal Systems. Journal of Chemical Theory and Computation, 13(8), 3731–3745. https://doi.org/10.1021/acs.jctc.7b00168 http://jultika.oulu.fi/Record/nbnfi-fe201801031039