The charger of a Li-Ion battery uses a constant voltage for charging the battery.
The battery voltage will rise to the maximum battery voltage (in our diagram 4.2V) and then remain at a constant charging voltage, while the charging current slowly decreases. Once the current fell under the threshold value (80 mA in our example) the charger stops.
If you want to upgrade the battery of your notebook from a Ni-Cad/Ni-MH battery to a Li-Ion battery, you have to check with your notebook vendor if the charger inside your notebook can support that battery type.
Besides the weight and volume advantage of Li-Ion batteries, there's also the missing memory effect. This is a condition that occurs when a battery is charged to the same level several times. The battery develops a chemical memory of that level and will not allow a full charge beyond that point. Li-Ion batteries don't have this problem. The only disadvantage of this battery type is the fact that it doesn't like low temperatures.