There are many different chemistries, I've personally used LiFePo4 and LiPo:
These are known as "duct tape batteries", for obvious reasons. (Really, they should be called Gorilla Tape batteries!)
The 6 old (but thoroughly proven and battle hardened) hand built batteries to the left are based on A123 M1 LiFePo4 (Lithium Iron Phosphate) cells. Each LiFePo4 battery in the pic contains 30 M1 cells, each cell is (nominally) 3.3V with a capacity of 2.3Ah. Each pack is configured as 6 cells in series (~19.8V) , 5 in parallel (11.5Ah). I always these use packs in pairs. Each pack has an integrated 60 amp fuse.
The two right batteries are actually four Pulse Battery ~22.2V RC LiPo (Lithium Polymer) 5000 mah (5Ah) brick batteries (each pair is taped together). Four of these LiPos give me ~44.4V with a capacity of 10Ah. I usually use 4, 6, or even 8 of these Lipo's at a time depending on the expected travel distance.
Energy wise, each of the 6 packs starting from the left each contain ~227 watt hours, for a total of 227*6=1.362 kilowatt hours of energy. The 2 LiPo packs on the right each contain ~231 watt hours of energy, for .462 kilowatt hours total. In practice only around 80-90% of the total energy is safely usable.
Back in the dark ages of ebiking, way back in 2007, getting good off the shelf ebike capable batteries proved extremely difficult. So I had to improvise and purchase a large amount of these awesome Dewalt 36 volt lithium power tool battery packs from ebay:
I was able to extract ten A123 M1 B cells from each of these power tool battery packs. I eventually purchased and took apart 18 of these guys to build the 6 packs in the pic above.
Carefully soldering my first LiFePo4 battery:
My first prototype battery was only 6 cells in series, 4 in parallel. I later added one more parallel group once I realized that 9.2Ah (2.3*4) just wasn't enough capacity.
Thankfully, with the easy availability of RC Lipo packs (at basically every decent RC hobby store) I don't expect to be hand building batteries any longer.