Some people have expressed an opinion that we will see a Moore's law for batteries. I think this is unlikely for two basic reasons: We've seen no such thing to date and batteries are not computer chips. Moore's law states that the density of transistors which can be put on an integrated circuit will double every 18 months, and so far it has held true. This has led to faster computer power and lower costs for electronics. What we've seen in lithium battery advances has mostly been steady advances of 5% a year with occasional jumps. I do expect we'll see more dramatic advances in the future as the sheer volume of research on the topic is increasing and none of the current chemistries are near their limits, to say nothing of future chemistries. Battery development is akin to squeezing a balloon, one end gets smaller while the other end bulges larger. Batteries have four parameters that need to be optimized, energy density, power delivery, useable life, (cycle and calendar), and safety. In batteries when you optimize for energy density you tend to decrease longevity, if you optimize for power you lessen energy density, and so on. The key is of course getting all these into one package, and ultimately at an affordable price, which really adds a fifth parameter just as important as the other four. It doesn't matter how good a battery is if it can't be produced at a reasonable cost. Unlike computer chips most of the costs of batteries are the high purity materials that must go into them. Advances come by using those materials in better ways, by finding better materials, and by improving the construction process. This mostly comes from constant research, trial and error, and tweaking and optimizing assembly lines to improve production yields.
A lot of work is being done in the field and there are very promising developments being announced on a regular basis but none as of yet has made it to market in an affordable product. I expect at some point some of them will and we will see a major jump in all battery parameters, but don't expect a steady doubling of all parameters every 18 months. Of course I'd be quite happy to be proven wrong in this case.