The interesting thing about Li-Poly batteries, when compared to Li-Ion, is that they have a much better weight/power ratio. So, if the Sikorsky Firefly, as linked by AlphaWolf would use those, it would need less and lighter batteries to fly longer.
And another interesting thing about Li-Poly batteries is, that they're basically Li-Ion ones, where the surface area of the cathode and/or anode are enlarged, by using a mesh-like surface instead of a flat solid.
Because, there is much more energy in batteries than is generally used or available, because at some moment the wattage required becomes larger than the wattage available. The cells aren't empty, far from that, but delivering the requested wattage would destroy them.
And that doesn't only depend on the chemical reaction mass inside, but also on the speed at which that reaction can happen. And a larger surface area means a faster speed. That's why Li-Poly cells seem to hold more power. They don't, they can mostly supply it faster, and thereby more of it before considered "empty".
And we can still go quite some way with that concept.
Basically, the energy density of Lithium batteries is great, it's only extracting it fast enough that is a problem. Which can be solved by high-tech Li-Poly cells.
Btw, Li-Ion packs as used in most applications, like laptops, are still only a set of cylindrical AA or AAA cells, encased in steel, linked together. Because that's much cheaper than making a custom one. Pouch cells, like found in cell phones are much better: no empty space inside, no heavy steel casings and made in a better (higher voltage) form factor. Li-Poly cells are generally only sold in pouch form.