There's also 21700's as well, with ICR chemistry for the really high discharge that bat-cookers can use. Vaping seems to be pushing these into mainstream availability.
Interesting news about vaping driving development of certain batteries.
Caving lights have always been far too small a niche market for battery manufacturers to produce dedicated products, so caving lights have always had to use whatever batteries are commercially available.
Remember 4.5 volt flat pack batteries, as used in the original Petzl Zoom and a number of pre-Li-ion caving lights? This battery was mainly produced for cycle lights: its use in walkers' headlights and caving lights was a reaction to its prior availability.
The stainless steel nicad cells (actually nickel-iron but they were always termed nicads) that were, in the early and mid 1980s, used to make high capacity (long lasing, low output) caving lights by dropping them in pairs in parallel into old Oldham and Exide 'R-type' battery cases were ex-MOD tank starting batteries (larger numbers in series). It was mere happenstance that two of their sizes exactly fitted mining battery cases.
Excluding belt-mounted carbide generators, the first lights developed specifically for caving (as opposed to cavers using mining lights), and produced in commercial quantities (as oppose to tiny batches and one-offs) was the lead-acid FX2, developed in about 1982-83. It was the availability of Li-ion batteries, LEDs, etc, that resulted in the later caving light revolution.
And what a revolution it was - after changing to a Fellows light, I could never go back to older lights - they seemed like groping around with a candle in a jam jar in comparison.
So what cavers need is for major mainstream uses for batteries (and LEDs) to continue to drive improvements, resulting in batteries that are, merely coincidentally, of high capacity and useful size for our very niche use. Oh, and for Roy to continue to combine them into superb cost-efficient lights.