@ElectricFlyer
It is theory: this is a short but descent summary:
Lithium–air battery - Wikipedia
The lab in Japan based on the published paper has demonstrated the first "reusable" Lithium-Air battery that I have read about. There might have been others, but in any case, the Japan lab demonstrated an energy density roughly five times higher than current generation.
@Jay Kempf
In an ICE combustion event, we theoretically have access to every atom. This is a significant reason so much raw theoretical power is actually released (how much is converted to useful energy is a separate debate, we do access very close to the peak of what is theoretical). While in battery tech, you will find that we access very little of the theoretical energy, often due to the thickness of the anode/cathode layers along with the mass taken up by the electrolyte.
If you look at the advances over the past decade from Panasonic, LG, GM, Ford.... the advances are significantly more on the production side by reducing the amount of raw materials used to produce the same power. We still have a long way to go on this front in terms of producing reliable and well known/understood battery management systems.
At this point, battery tech is closer to the early 1900s for the ICE engine when fires and other issues were "common". In fact ICE had a significantly rougher start than batteries have, it is just that most of us have forgotten the history and have built a reservoir of knowledge to prevent these issues for ICE. This journey for battery tech is effectively just starting.
Tim