We discuss the electrochemicalreactions at the oxygen electrode of an aprotic Li-air battery. Using density functional theory to estimate the free energy of intermediates during the discharge and charge of the battery, we introduce a reactionfree energy diagram and identify possible origins of the overpotential for both processes. We also address the question of electron conductivity through the Li 2 O 2 electrode and show that in the presence of Li vacancies Li 2 O 2 becomes a conductor.