What is a Lithium-ion battery?
Lithium is the lightest of all metals, has the greatest electrochemical potential and provides the largest energy content. The lithium ion battery makes use of lithium cobalt oxide (which has superior cycling properties at high voltages) as the positive electrode and a highly-crystallized specialty carbon as the negative electrode. It uses an organic solvent, optimized for the specialty carbon, as the electrolytic fluid. Rechargeable batteries using lithium metal as the negative electrodes (anode) are capable of providing both high voltage and excellent capacity, resulting in an extraordinary high-energy density.
What is the difference between Lithium-Ion and Lithium-ion polymer?
Lithium-ion uses a liquid or gel type electrolyte that requires substantial secondary packaging to safely contain flammable active ingredients. This additional packaging not only increases the weight and cost, but it also limits the size flexibility. There is no free liquid electrolyte in Lithium-ion polymer technology. As a result, batteries are packaged in a foil. This provides added weight benefits and design flexibility. To make short, polymer is a flatpack while lithium ion is more battery(d, c, AA, AAA, ect.)
Structure
The lithium ion battery has a three-layer, coiled structure within its case. These three layers are comprised of a positive electrode plate (made with lithium cobalt oxide as its chief active ingredient), a negative electrode plate (a specialty carbon), and a separator layer. The battery is equipped with a variety of measures to insure safety, along with an anti-explosion valve that releases gas if the internal pressure exceeds a specific value, thereby preventing the battery from exploding.
Do not disassemble or modify the battery. Damaging this circuit may cause overheating, ignition, bursting, and/or breaking of the battery(these points also apply to Ni-Cd/Ni-MH).
Lithium-ion batteries fail due to excessive low discharge. If discharged below 2.8 volts per cell, overcharged, or short circuit the internal safety circuit opens and the battery appears dead. A charge with the original charger is no longer possible. Some battery analyzers (Cadex) feature a boost function that reactivates the protection circuit of a failed battery and enables a recharge.
Pros
High Energy Density : Because the lithium ion batteries are high voltage/light weight batteries, they boast a higher energy density than rechargeable nickel cadmium (Ni-Cd) or nickel metal hydride (Ni-MH) batterise.
High Voltage: Lithium ion batteries produce 3.7 volts, approximately three times the voltage of recargeable Ni-Cd or Ni-MH batteries. This makes it possible to make smaller, lighter equipment.
No Memory Effect : The battery "forgets" what full charge is like and even after hours of charging will not hold the same level of power that it used to. Having said that all rechargeable batteries degrade over time, even lithium ion. However lithium ion batteries tend to "go" all at once, where one day they are working fine and the next they simply won't hold any charge. This will usually occur only after at least a couple of years or damage, but can occur sooner if you allow the battery to completely discharge.
Cons

More expensive

Greater care is needed

More precise equipment and monitoring required

large size (I have not seen a "AAA" size lithium or smaller)
Safety precautions for Lithium Ion batteries
1. Never charge Lithium Ion cells/packs at any rate unattended.
2. Only charge LIthium Ion cells/packs with a charger designed specifically for Lithium Ion chemistry.
3. Lithium Ion cells can ignite because of unmatched cell capacity or voltage, cell damage, charger failure, incorrect charger settings and other factors.
4. Always use the correct charging voltage. Lithium Ion cells/packs may ignite if connected to a charger supplying more than 6 volts per cell.
5. Always assure the charger is working properly.
6. Always charge Lithium Ion cells/packs where no harm can result, no matter what happens.
7. Never charge a cell/pack on a wooden workbench, or on any flammable material.
8. If a cell/pack is involved in a crash:
a. Remove the cell/pack from the model.
b. Carefully inspect the cell/pack for shorts in the wiring or connections. If in doubt, cut all wires from the cell/pack.
c. Disassemble the pack.
d. Inspect cells for dents, cracks and splits. Dispose of damaged cells
9. Handle all cells/packs with care, as they can deliver high currents if shorted.
10. Always store cells/packs in a secure location where they cannot be shorted or handled by children.
11. When constructing a pack, use only cells of the same capacity (mAh).