I have been contributing to the comments section of this article on battery safety. Battery fires from cheap lithium-ion batteries are a genuine hazard, as I know from flying RC aircraft.
Learn what causes Li-ion to fail and what to do in case of fire. Battery makers are obligated to meet safety requirements, but less reputable firms may cheat.
Batteries in brand-name electronics (such as phones and laptop computers) with built-in charging systems are well made and are very safe unless physically damaged e.g. in a car crash. But cheap batteries, which some people are starting to use in flashlights and vaping devices, are much riskier. Among other cautions, do not charge freestanding lithium-ion batteries unattended. The house you save may be your own.
Here is the site’s home page, which covers far more than safety. http://batteryuniversity.com/learn/