LiIon polymer cells should not be taken above 4.2 vdc. LiIon charger is constant current with voltage limiter to cap the voltage at 4.2 vdc per cell. There is also a minimum voltage of about 2.8-3.0 vdc before full constant current charge is applied.
If battery is less then 1.5vdc, it is bad and should not be charged. Between 1.5vdc and 2.8vdc the charge current is limited to about 0.05 C rate.
LiIon batteries do not take overcharge which creates problems with series connected cells. As cell state of charge diverge over time between series connected cells, some cell may reach 4.2 vdc point before other cells in the series stack. Series battery packs have bleeder circuits that help keep individual cells from getting overcharged before other cells in the battery pack have achieved full charge.
Charge is terminated when cell has reached 4.2 vdc and current has tappered off to about 0.02 C to 0.05C current level. Cell charge current should not be greater then 0.5C to 0.7C rate. It takes about 2.5 hours to fully charge a LiIon polymer battery. You can achieve about 85% charge within an hour.
Cells should not be allowed to be discharged below 2.1 vdc to 2.8 vdc, depending on discharge current rate, to prevent damage to cell. Cellphone and laptop battery packs have a series MOSFET to disconnect battery when voltage drops below this level to avoid permanent damage to cells.