The lithium-air battery (LAB) is arguably the battery with the highest energy density, but also a battery with significant challenges to be overcome before it can be used commercially in practical devices. Here, we discuss experimental approaches developed by some of the authors to understand the function and failure of lithium-oxygen batteries. For example, experiments in which nuclear magnetic resonance (NMR) spectroscopy was used to quantify dissolved oxygen concentrations and diffusivity are described. 17O magic angle spinning (MAS) NMR spectra of electrodes extracted from batteries at different states of charge (SOC) allowed the electrolyte decomposition products at each stage to be determined. For instance, the formation of Li2CO3 and LiOH in a dimethoxyethane (DME) solvent and their subsequent removal on charging was followed. Redox mediators have been used to chemically reduce oxygen or to chemically oxidise Li2O2 in order to prevent electrode clogging by insulating compounds, which leads to lower capacities and rapid degradation; the studies of these mediators represent an area where NMR and electron paramagnetic resonance (EPR) studies could play a role in unravelling reaction mechanisms. Finally, recently developed coupled in situ NMR and electrochemical impedance spectroscopy (EIS) are used to characterise the charge transport mechanism in lithium symmetric cells and to distinguish between electronic and ionic transport, demonstrating the formation of transient (soft) shorts in common lithium-oxygen electrolytes. More stable solid electrolyte interphases are formed under an oxygen atmosphere, which helps stabilise the lithium anode on cycling.