We describe Li–O2 discharge experiments in a bulk electrolysis cell as a function of current density and temperature. In combination with a simple model, these imply that charge transport through Li2O2 in Li–O2 batteries at practical current densities is based principally on hole tunneling, with hole polaron conductivity playing a significant role near the end of very low current discharges and at temperatures greater than 30 °C. We also show that charge-transport limitations are much less significant during charging than those in discharge. A key element of the model that qualitatively explains all results is the alignment of the Li2O2 valence band maximum close to the electrochemical Fermi energy and how this alignment varies with overpotentials during discharge and charge. In fact, comparison of the model with the experiments allows determination of the alignment of the bands relative to the electrochemical Fermi level.