Disclosed herein are embodiments of lithium/air batteries and methods of making and using the same. Certain embodiments are pouch-cell batteries encased within an oxygen-permeable membrane packaging material that is less than 2% of the total battery weight. Some embodiments include a hybrid air electrode comprising carbon and an ion insertion material, wherein the mass ratio of ion insertion material to carbon is 0.2 to 0.8. The air electrode may include hydrophobic, porous fibers. In particular embodiments, the air electrode is soaked with an electrolyte comprising one or more solvents including dimethyl ether, and the dimethyl ether subsequently is evacuated from the soaked electrode. In other embodiments, the electrolyte comprises 10-20% crown ether by weight.