Lithium batteries have not been known for "a hundred years", but barely half that. Since Mr. Anon quoted Wikipedia, this article (http://en.wikipedia.org/wiki/Lithium_ion_battery) states clearly that the first lithium ion battery design was made available in the 1960s, and (quoted) "the first commercial lithium ion battery was released by Sony in 1991".
Lithium metal batteries have been in existence for quite a while longer, but I doubt there is any inherent instability in them, otherwise they would probably not be used in pacemakers.
The battery itself has, of course, a long history that goes back to Mr. Volta in the year 1800 (http://www.batteryuniversity.com/partone-2.htm). It is nothing short of astonishing to read that the fuel cell was invented in 1839, the lead-acid battery in 1859, and the nickel-cadmium that we all know in 1899.
Battery technology that is still used today was invented more than a century ago, but the most recent lithium technology is a refinement that is a lot younger than the rest of the field.