Lithium batteries hold a lot of energy for their size. That's a good thing for powering a laptop, but bad if something were to go wrong. The reaction that releases electrical energy is unstable: it releases heat, and heat causes the reaction to go more quickly... which releases more heat... which causes more energy released, and so on. If the reaction isn't controlled, all of the energy can be released in less than a second, leading to a fire or even an explosion. Things like discharging too quickly, overcharging, punctures, and internal short circuits can all cause a battery to fail this way. So lithium battery manufacturers add several stages of safety measures to make sure nothing goes wrong. Some have even shot holes through a fully charged battery to make sure it wouldn't explode. But there have been a lot of problems in recent years with counterfeit batteries, which look like "proper" batteries from the outside (Dell, Apple, Sony, whatever) but are not made with the same safety measures. If you're shopping for a battery and you find a price that's too good to be true, it's probably too good to be true!

Lithium polymer batteries are about the same as lithium ion batteries as far as safety is concerned. They operate with nearly the same chemistry, but using a gel rather than a liquid. Both types have vents to prevent buildup of excess pressure.

Lithium polymer batteries could potentially be dangerous.There are often very corrosive chemicals inside batteries, and it would be very bad for these chemicals to get into the environment, or consumed by a person or animal. However, if care is taken to store the batteries properly, Lithium batteries shouldn't be very dangerous at all.

Additionally, Lithium polymer batteries should be even safer than traditional Lithium batteries. Polymers are used in the batteries to make the batteries more resistant to damage, which helps keep the dangerous chemicals from leaking.