This could be the breakthrough we're waiting for:
IBM Creates 'Breathing' High-Density Lithium-Air Battery - Slashdot
IBM creates breathing, high-density, light-weight lithium-air battery | ExtremeTech
IBM - The Battery 500 Project - United States
The main thing, though, is that lithium-air energy density is a lot higher than conventional lithium-ion batteries: the max energy density of lithium-air batteries is theorized to be around 12 kWh/kg, some 15 times greater than li-ion — and more importantly, comparable to gasoline."