If one has ever dismantled a mobile phone they will have noticed, almost instantly, which component takes up the most space. This would be the battery, the essential component of any portable electronic device and despite microchips being a tenth of the size they were ten years ago, batteries have decreased is size by about 17%, not very much at all. Also with a shunt towards renewable power coming from the sun and the wind our sources of energy are going to become more intermittent. Being able to store energy efficiently on a personnel device and also on a national grid scale is essential for our future developments.
Some advancements come from a complete switch up of energy storage. Instead of using chemical stores like in regular batteries capacitors can store energy as part of the electrostatic repulsion between the two plates. The more charge pumped on to one plate the harder it is to put any more charge on so very high voltages would be needed. This using banks of massive capacitors could one day be used as a storage method by the national grid. By varying the resistance of the circuit the capacitors applied to the rate of discharge can be quickened or slowed to meet demand. But it is very unlikely people would ever want to carry around a 10000V plate in their phone so capacitors are unlikely to be helpful here. In this case it is better to simply improve batteries we already have even at a slow rate. For instance using lithium cobalt oxide (LiCoO2) in regular lithium ion batteries can increase power performance and battery life along with other elements like germanium. By using slightly different materials in slightly different orientations incremental improvement can be made which will eventually lead to either the desired result or a breakthrough.