The charging current is limited by the charging IC/schematic inside the charger. Preferably, charge Li batteries with their own charger (the one that came with the appliance), or with a compatible charger specified by the battery/appliance producer.
Apart from that, most Li-Ion cells (i.e. mobile phones batteries) have a small protection board inside the battery itself, usually on the same PCB where the contacts are, with a dedicated IC and a (thermal) fusible. The inside protection circuit is supposed to disconnect the battery against damage conditions:
- at over discharge (less than 2.8V or so)
- at over charge (more than 4.3V or so)
- at over current/short-circuit
In normal use, the charger IC is the one that limits the max voltage and the max charging current applied, while the appliance is supposed to limit the max discharging and shut down before the minimum voltage is reached.
In fact, it is not unusual to have a smaller charging current at lower voltage (less than 3.5V or so), than a nominal charging current until the top voltage is achieved (4.1-4.3V or so, depending on the cell type), then a 3rd phase of constant voltage for a limited time (it is not good to keep Li-Ion at their max voltage for long periods of time).
Sometimes, after the appliance shut down, the battery might keep going discharged slowly, and after a while the internal battery protection will disconnect it (has a series MOSFET inside, between others), and the battery will measure 0V. If you put it in the charger, after a couple of minutes the protection circuit will disarm and the battery will start charging normally. So, if a battery shows 0V, don't abuse it by connecting the battery to higher voltage, as sometimes advised online. Just let it charge normally, with its own charger, and be patient.