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Stories of exploding lithium ion (LiIon) batteries in laptops appeared around 2006. In 2006 the U.S. Consumer Product Safety Commission reported only 43 laptop fires in the United States since 2001, or about 10 every year.
Some research has been done on the problem but as of 2013 it still existed.

When overheated batteries forced a 787 to make an emergency landing in 2013, people grew really concerned.

There are about 130,000,000 laptops in the US.
There are about 10 battery fires/explosions per year.
Your chance of a problem is 1:13 Million

"You're far more likely to be struck by lightning (1 in 1,042,000) than ever see a battery flame up (1 in 10 million is the number experts tend to quote)."
Source: The lithium-ion battery that didn't explode - CNET, 2018

If the battery gets hot through use or recharging, little pieces of lithium metal (remnants of manufacturing) can move around in the liquid medium in a pressurized container, much like grains of rice in a pot of water. If a piece of metal gets too close to the separator between the anode and cathode, it can puncture the separator and cause a short circuit. There are a few possible scenarios for what can go wrong in the case of a short circuit:

• If it creates a spark, the flammable liquid can ignite, causing a fire.
• If it causes the temperature inside the battery to rise rapidly, the battery can explode due to the increased pressure.
• If it causes the temperature to rise slowly, the battery can melt, and the liquid inside can leak out.

There is certainly the specific case that started all this with Dell and I think what's out there is probably the very likely case is what Dell is saying is that in the Sony battery manufacturing process, some contaminates were introduced into the cells of the battery that allowed them to short out and overheat.
Playing with Fire: Part II | PSpitstop.com

In June 2013 Best Buy recalled ATG Replacement Batteries for the MacBook Pro.
Model numbers Model number "MC-MBOOK13B" and Model number "MC-MBOOK13W"
See Best Buy Recalls ATG Replacement Batteries for the MacBook Pro Due to Fire, Burn Hazards (Recall Alert) | U.S. Consumer Product Safety Commission (CPSC)

What to do:
Lithium batteries have a built-in smart protective circuit, which stops current flow to the battery when it is fully charged.
Unlike most other consumer batteries, LiIon batteries will suffer permanent damage if charged down completely. That's why laptop computers shut down before the battery is completely run down.
So you should not have to worry about human error in charging.

If your laptop gets exceedingly hot while charging or if it starts to smoke, unplug it and move it to a safe place for 15 minutes.

If it actually catches on fire, it is an electrical and metal (lithium burns), so you need a Class D fire extinguisher.
A lithium fire is hot enough to break down water and produce hydrogen gas, or strip the Oxygen from CO2 so NEVER THROW WATER ON IT or use a Carbon Dioxide extinguisher.

Class D (dry powder [Different than dry chemical]) extinguishers are expensive (>$400).
If you are storing a bunch of batteries you may want to have a bucket of dry sand or table salt near by.

Links:
These lithium-ion batteries can't catch fire because they harden on impact -- ScienceDaily 2018
Summer of the exploding laptop! | CBC News 2006
Notebook PC Explodes | PSpitstop.com
Exploding Battery Panic!
Fire Safety with Lithium and Lithium Ion batteries - Laser Pointers