Solid-state nuclear magnetic resonance (ssNMR) is a powerful element-specific technique to study local atomic environments in many different classes of materials; however, ssNMRbased methodologies have primarily focussed on diamagnetic systems without any unpaired electrons. In paramagnetic or metallic materials localised or delocalised unpaired electrons, respectively, couple with the nuclear magnetic moments and introduce significantly greater spectral broadening, often combined with very fast nuclear relaxation, so that these systems are challenging to study. However, these same hyperfine interactions can also provide important details of the electronic and magnetic structure for a sample. In this work ssNMR methodologies are developed to study different paramagnetic and metallic systems, and thereby demonstrate the information that can be obtained. These strategies include investigating the temperature dependence of the NMR spectra, to distinguish paramagnetic and metallic shifts, and exploiting differences in relaxation rates to afford spectral selectivity and extract further information. Specifically, the following studies have been performed: 1) The 17O NMR of Sm2O3, Eu2O3 and Sm/Eu-substituted CeO2, for which the lanthanide ions induce paramagnetic shifts with unusual temperature dependences due to the presence of low-lying excited electronic states. The spectra of the monoclinic polymorphs of the sesquioxides are assigned and the paramagnetic shifts of the cubic polymorphs are investigated over a wide temperature range. Different local environments in the substituted CeO2 are identified due to nearest-neighbour lanthanide ions and oxygen vacancies, and the activation energy for oxygen motion is determined from variable temperature T1 measurements. 2) The surface-selective direct 17O dynamic nuclear polarisation (DNP) NMR of CeO2 nanoparticles. In this case exogenous paramagnetic biradicals are deliberately introduced and exploited to selectively hyperpolarise the surface of CeO2, so that the first three (sub-)surface 17O environments can be identified with high specificity. Polarisation build-up curves show that this selectivity is due to faster polarisation of the surface relative to the bulk. 3) The structure and mechanism of electrochemically metallised VO2. By comparison with catalytically hydrogenated VO2, electrochemical metallisation is shown to be associated with hydrogen intercalation, and the presence of metallic and paramagnetic phases is explored with 1H, 2H, 17O and 51V NMR. By selectively deuterating the ionic liquid electrolyte, hydrogenation is then shown to arise from electrolyte breakdown, and the degree of hydrogenation and resultant phases are investigated as a function of the particle size and the temperature of electrochemical metallisation.