Here you can find the structures and lithium diffusion animations of different materials used in lithium ion batteries (LIB). LIBs have drawn a lot of attention recently due to important applications in consumer electronics and electric vehicles. LIBs represnt a significant step to the goal of building a zero-emission society.
When the battery is being charged, Li+ ions move from the cathode via the electrolyte to the anode.
Electrons simultaneously move to the anode via the external electric circuit.
When the battery is being discharged, Li+ ions move from the anode via the electrolyte to the cathode.
Electrons simultaneously move to the cathode via the external electric circuit.
When the battery is working (or discharging), the cathode is being reduced and the anode would be oxidised. When the battery is being charged, the process is reversed. The cathode is forced to be oxidised (by external voltage because the charging reaction has positive ΔG) and the anode is being reduced.
Further reading on battery, fuel cell and supercapacitor technology:
M. Winter and R. J. Brodd, Chem. Rev., 2004, 104, 4245-4270.