Although they don't necessarily follow Moore's law, batteries have still gotten smaller and more efficient as the years pass. The current go-to power cell of choice is the lithium-ion battery. It's already quite small as it is, but some scientists think it can get even smaller. How small? Try nanometers.
Well, it looks like this is one aspect of fictional robotics that's starting to catch up with reality. Researchers at Arizona State designed a system that lets synthetics recreate the natural healing process found in organics. It uses shape-memory or mimetic polymers embedded with a network of fiber optics. The network senses any damage to the system, then delivers heat to the "wounded" area to repair it.