Rechargeable energy storage systems with high energy density and round-trip efficiency are urgently needed to capture and deliver renewable energy for applications such as electric transportation. Lithium–air/lithium–oxygen (Li–O₂) batteries have received extraordinary research attention recently owing to their potential to provide positive electrode gravimetric energies considerably higher (3 to 5×) than Li-ion positive electrodes, although the packaged device energy density advantage will be lower (2×). In light of the major technological challenges of Li–O₂ batteries, we discuss current understanding developed in non-carbonate electrolytes of Li–O₂ redox chemistry upon discharge and charge, oxygen reduction reaction product characteristics upon discharge, and the chemical instability of electrolytes and carbon commonly used in the oxygen electrode. We show that the kinetics of oxygen reduction reaction are influenced by catalysts at small discharge capacities (Li₂O₂ thickness less than 1 nm), but not at large Li₂O₂ thicknesses, yielding insights into the governing processes during discharge. In addition, we discuss the characteristics of discharge products (mainly Li₂O₂) including morphological, electronic and surface features and parasitic reactivity with carbon. On charge, we examine the reaction mechanism of the oxygen evolution reaction from Li₂O₂ and the influence of catalysts on bulk Li₂O₂ decomposition. These analyses provide insights into major discrepancies regarding Li–O₂ charge kinetics and the role of catalyst. In light of these findings, we highlight open questions and challenges in the Li–O₂ field relevant to developing practical, reversible batteries that achieve the anticipated energy density advantage with a long cycle life.