The development of rechargeable batteries with higher energy densities and longer lifetimes represents a major challenge in enabling the shift from fossil fuel-powered to electric vehicles. Preventing the parasitic reactions between the electrodes (positive and negative) and the electrolyte solution, is essential for enabling longer lasting lithium-ion batteries. In this work, solution- and solid-state nuclear magnetic resonance (NMR) methodologies are developed for studying the electrode-electrolyte reactions. The decomposition reactions of the electrolyte solution at positive electrodes, layered transition metal oxides (LiMO2, M = Ni, Mn, Co or Al, e.g. LiCoO2, LCO; LiNixMnyCo1-x-yO2, NMC), are investigated by a combination of solution NMR spectroscopy and operando gas measurements. The soluble products formed at LCO electrodes are identified, and reaction mechanisms are proposed to rationalise the formation of the observed species. The proposed mechanisms are confirmed by isotopic labelling and by comparing the decomposition products formed at the positive electrode to those formed in a controlled setup simulating specific battery conditions. This methodology is then extended to NMC electrodes with various compositions (i.e., different ratios of Ni, Mn and Co), which revealed that the mechanisms for electrolyte decomposition were the same for all compositions, but the onset voltage for the Ni-rich materials was lower. At the negative electrode, the reduction and deposition of the electrolyte solution at the metal surface results in the formation of a passivating layer, the solid electrolyte interphase (SEI). The interface between a lithium metal electrode and the SEI is studied by dynamic nuclear polarisation (DNP) enhanced solid-state NMR. The signals from SEI components are selectively enhanced in 1H, 7Li and 19F NMR spectra via an Overhauser DNP mechanism, and the proximity of the SEI species to the metal can be inferred from the relative DNP enhancements of the signals. The effect of temperature, magnetic field strength, microwave power and sample dilution on the enhancement are also explored, to understand what the limitations are when using this mechanism to study the lithium metal-SEI interface.