In the search for improved energy storage, rechargeable metal-oxygen batteries are very attractive owing to their reliance on molecular oxygen, which forms oxides on discharge that decompose reversibly on charge. Much focus has been directed at aprotic Li-O2 cells, but the aprotic Na-O2 system is of equal interest because of its better reversibility. We report here on the critical role and mechanism of phase-transfer catalysis in Na-O2 batteries. We find that it is solely responsible for the growth and dissolution of micrometre-sized cubic NaO2 crystals and for the reversible cell capacity. In the absence of phase-transfer catalysis, quasi-amorphous NaO2 films are formed and cells exhibit negligible capacity. Electrochemical investigations provide a measure of the transportation of superoxide from the carbon electrode to the electrolyte phase by the phase transfer catalyst. This leads to a new understanding of the mechanism of Na-O2 batteries that, significantly, extends to Li-O2 cells and explains their different behaviour.