Lithium ion battery packs are made up of thin sheets of active material seperated by thin sheets of insulator containing an electrolyte. As the battery ages and with repeated charge discharge cycles, tiny metal dendrites grow out from the surface of the active material. If the dendrites penetrate the insulation layer, a short circuit forms inside the battery. Depending on the thickness of the dendrite, sufficient heat can be generated to boil the electrolyte and the steam causes the battery pack to swell. In many cases, the pack swelling will break the short circuit and prevent further damage and risk of fire.
If the pack splits and the contents become exposed to air then any metallic lithium can spontaneously combust. The actual amount of lithium metal in phone and camera type battery packs is generally very limited, so any small fires are also usually limited, especially if the battery remains contained inside the equipment.
As battery packs age, they sometimes become hot during charging as small dendrites form and are burnt away. The battery capacity may also appear reduced. This is the first sign that the pack has reached the end of its life and should be replaced. Modern packs are good for between 300 and 500 complete charge cycles, or about 3 to 5 years of normal use.
Metal cased batteries tend not to swell when they overheat due to internal short circuits, but they are fitted with safety valves to release internal pressure. There may be some electrolyte leakage if sufficient internal damage occurs. Again, the primary sign of problems developing is that the battery becomes hot during charging.
All batteries become warm during charging cycles. The difference between a healthy battery and one at the end of its life is that the healthy battery will feel just warm to the touch. A failing battery will feel uncomfortably hot, probably around 60°C or possibly more. The internal temperature of the battery can be assumed to be rather hotter than any surface exposed to the air, so high temperatures can be indicative of the internal electrolyte reaching temperatures close to boiling at which point damage is definitely going to occur.
Lithium ion batteries have the advantage of very high energy density. A typical laptop battery pack can contain the same energy as a fully charged car battery in a package a fraction the size and weight of a lead acid cell. The energy density is so high and the weight savings are so great that they are now used in aircraft despite the extra safety systems and heavy containment boxes needed to house them.