This thesis presents a combined experimental and theoretical approach on studying Mg-ion battery electrode materials, where Nuclear Magnetic Resonance (NMR) spectroscopy plays a central role in identifying the local structure and dynamics of the magnesium ions. Density Functional Theory (DFT) techniques are used extensively to (i) calculate and rationalise the observed NMR shifts, (ii) provide insights into the dynamics involved in such electrode materials, and (iii) guide the synthesis of candidate electrode materials. This work begins by a systematic study of 25Mg solid-state NMR in paramagnetic oxides, where the presence of transition metals makes them suitable for applications in high-voltage cathode materials. DFT methods for predicting and rationalising the paramagnetic NMR shifts are developed, with experimental verifications on synthesised samples. Feasibility of using advanced NMR pulse sequences such as Rotor-Assisted Population Transfer and Magic Angle Turning is demonstrated on such systems to afford enhanced resolution and sensitivity. This approach of combined NMR and DFT techniques is then applied to two of magnesium vanadates for high-voltage cathode applications. In particular, DFT-based thermodynamic energies are used to rationally design the synthetic steps leading to the said vanadate materials, followed by DFT prediction of the migration barriers. The prepared material was subject to experimental characterisation using NMR and diffraction techniques, with an initial cycling data in an electrochemical cell. In the final part, a combined experimental and ab initio investigation on Mg3Bi2, a promising Mg-ion battery anode material, is presented. Previous reports on variable-temperature 25Mg NMR spectroscopy is validated by DFT calculations on the migration barrier and defect energetics. Mechanistic insights on the migration mechanism are presented using the hybrid eigenvector-following transition state searching method, where the relativistic effects of heavy bismuth is shown to influence the migration barrier. We show that the defect formation energy of a Mg vacancy is critical in the apparent Mg diffusion barrier, which is heavily influenced by sample preparation conditions.