I think I’m almost done learning about flashlights. This weekend I researched lithium ion batteries and how they relate to flashlights. This is because the tiny flashlight I bought can be powered by a lithium ion battery, though it is not recommended (this is different from disposable lithium batteries like Energizer sells that you only use once but have more power than alkalines). But if you put one in there it will make the flashlight much brighter (and potentially burn it out if you leave it running for very long on the highest brightness setting). One problem with Li-ion batteries is they tend to explode or catch fire. Just about all of the cases where laptops, iPods, or other devices catch fire are because of Li-ion batteries. Many Li-ion batteries come with circuit protection that is supposed to kick in if the voltage of the battery gets too high or if it gets too low (both are bad).
There are a lot of different sizes of Li-ion batteries denoted with a number that tells you the diameter, length, and shape. For instance the battery that replaces a AAA battery is called a 10440 which breaks down to 10 mm diameter, 44 mm long, and 0 for a round shape. These batteries are too small to include protection circuits. Most of the batteries supply 3.6 (or 3.7) volts nominally but you charge them 4.2 volts and they need to be recharged when they get down to 2.8 volts or something like that. Because they are supplying more than twice the voltage of a regular 1.5 volt alkaline or 1.2 volt NiMH battery, it makes sense they will be brighter. But you have to make sure you get a flashlight that is made for that higher voltage.