In common consumer batteries, we saw the following evolution:

• Dry-cell (zinc-carbon) batteries (late 1800s) - having a non-liquid electrolyte, these can be transported and used inside portable devices. They perform so poorly in sustained use that they led to the name "flash light" for the short runtime of portable lighting using them for power.
• Heavy-duty (zinc-chloride) (late 1800s) - an improvement to dry-cell chemistry that roughly quadrupled runtime under load. Still used today for ultra-low-cost batteries.
• NiCD (1940s) - a rechargeable substitute for zinc-chloride. Superior performance under extreme load, but otherwise low capacity, prone to memory effects, and a source of toxic waste.
• Alkaline battery (1960s) - a roughly eightfold improvement over zinc-carbon under load, still very common today.
• Lithium battery (1970s) - much more capable of sustaining high loads than alkaline, extremely shelf-stable, expensive
• NiMH battery (1989) - a major improvement over NiCD, offering a rechargeable substitute with similar capacity to alkaline under light load and far superior performance under heavy load without the memory effect and toxicity of NiCD.
• Low-self-discharge NiMH (2005) - Improvements in shelf-stability made pre-charged rechargeable batteries commercially viable, and allow users to store spare rechargeables charged.

And then there's the lithium-ion rechargeable. You're probably reading this on a device powered by one. It's much lighter than NiMH for the same amount of energy storage, and a bit better on energy per volume as well. Since its introduction in 1991, Li-ion technology has dropped in price by a factor of about 25, which is why electric cars are commercially viable now and weren't a couple decades ago.

Unfortunately, consumer devices powered by standardized, field-replaceable Li-ion cells haven't really caught on outside of vaporizer hobbyists and flashlights.