Lithium Ion (li-ion)
Warning! Charging batteries without due care can cause the battery to swell and even explode. The information presented here is basic and should only be used as a rough guide in combination with other sources. When in doubt, set your charge rates low and increase only through successful experience.
Higher energy density by volume and weight than any other battery chemistry. Lithium ion and other lithium based chemistries have become the backbone of modern portable technology. Battery life is also fairly good at around 500 full cycles, although performance of course varies on a number of factors. Like most rechargeables, you can get more than the equivalent full cycles by limiting the depth of discharge. For example if you limit your depth of discharge to 50% battery capacity, you'll get the equivalent of 1500 full cycles.
Charging is fairly straight forward. Just charge the battery until it hits 4.2 volts. Some variations are slightly different in the charge voltage so be sure to read the battery spec (ie some are 4.0 volts). Although the max charge voltage is 4.2, the battery is said to have a mean output of 3.6 volts. The battery is considered to be discharged at around 3.0 volts but it can go much lower. If you do go lower though you risk damaging the battery.
The rate of charge is around the same as the capacity (ie 2000mA hours = 2 amp charge rate). Many newer models though can handle much higher rates though so if you're impatient, check the spec. If you don't stop charging at 4.2 volts (or charge too fast) the battery will swell up and could explode. Lithium when exposed to air is, shall we say, energetic, so an exploding battery is not good. It's for this reason that lithium batteries of any kind are restricted on passenger aircraft when not installed in their final product.
Note that the rate of charge (the amount of current the battery absorbs) drops considerably as it nears its charge voltage. This is noticeable in that the charger will shut on and off as the battery hits full voltage and then drops again. There is as much as 20% more capacity still to go at this point, so make sure your charger is prepared for this.
Very low self-discharge rate, and excellent shelf-life. These batteries can sit waiting for 20 years or more and still be good to go.