Batteries are one of the biggest bottle-necks to more innovation with mobile devices. While there have been great strides in fast charging, batteries can't last longer without getting bigger, and there's a size limit to comfortable smartphones (though manufacturers could skew thicker for better battery rather than always going for thinness.) But, Sony may have made a bump.
The big change is rather than lithium-ion, which has been the standard for electronics batteries since 1991, Sony is working on a new high-capacity battery based on a sulfur compound. Normally, the electrode in sulfur-based batteries dissolves into the electrolyte too fast during each charging cycle, which decreases the capacity of the battery. But, Sony claims it has found the solution to this problem (double meaning alert!), and can build batteries with 40% more capacity using the sulfur compound.
This would mean that in the best case scenario, a phone like the Nexus 6P would be able to have a 4500mAh battery the same physical size as the current 3220mAh battery; the Samsung Galaxy S6 could have a 3750mAh battery rather than 2550mAh; and, the Apple iPhone 6 could have 2530mAh battery rather than 1810mAh.
Of course, it could also mean that manufacturers would make devices thinner and keep the same size batteries, but that possibility gets our rage spiking out of control.