The first battery was invented over 200 years ago and we have not made many big advancements since. We have switched out the elements we use and come up with some tricks to get better capacity but I would argue battery technology has not kept up with everything else. So what does the future hold and how can we keep advancing?
Tech keeps getting smaller and that makes it harder to get good battery capacity into our devices. Now we even have small wearable devices. The lithium polymer battery is our only real option but they still do not have the power capacity we would like to see. How many times have your devices run out of power on you?
Summary of battery History

Its always good to look at the past when thinking about the future. The first battery that could continuously provide electric current was the voltaic pile and it was invented in 1799.
After that not much changed for 60 years until the lead-acid battery was invented in 1859. The lead-acid battery is the first rechargeable battery and the same kind of battery that is in your car, truck, lawn mower, or countless other things. So, you are all using battery technology that was invented over 150 years ago!
Then you had your nickel based batteries like the nickel metal-hydride that was invented over 50 years ago in 1967.
Next we have the lithium batteries. Lithium batteries were invented over 40 years ago in the 1970s. In 1997 the lithium polymer battery was released and today that is what all smart phones use.
If you count the polymer battery as something new then the best you could say is nothing new has come from battery technology in 20 years. Now consider that the first iPhone came out in 2007.
Problems with Lithium batteries
Lithium is the best we have but it has its problems. A lithium battery will slowly degrade even if it is not being used. They are good for about 2 years. Some last longer but they will start to lose capacity until one day they just stop working. This is one reason it drives me crazy that I can’t find a smart phone with a replaceable battery. But that is a rant for another day.
Another problem they have is they can burst into flames. Not that long ago Samsung had to do a big recall on phones that were catching on fire. Even if you have a good battery it can still catch on fire if it is damaged.
Lithium also must have special circuits to charge them. If you tried to charge them with plain old reverse current it may catch on fire. At the very least you are going to mess it up.
Research is being done on a new Solid-state lithium-ion battery that will not overheat or catch on fire. But I do not think anything like that is in the market right now.
Fluoride-ion batteries
Lithium is the most electro-positive element but fluoride is the most electro-negative element. So researchers are trying to make a battery with fluoride that works in reverse. Power is just the flow of electrons and it does not matter what direction they flow in the battery. So a fluoride-ion battery would be able to provide power just like any other battery. Researchers also say it has the potential for ten times the energy density of lithium-ion batteries! That would be an amazing jump in battery technology.
Motion power
Because of all the short falls in modern batteries, some people are looking at other exciting ways to power devices. Motion power was one of the first techniques I seen. I believe it was the self-winding watch. A very cool idea. I never owned one but I remember wanting one just because I thought the idea was neat. Maybe we can put something in our shoes that will generate power as we walk?
Solar Power
Of course, there is also solar power. But you have the same problem with solar as you do batteries and that is that it takes a lot of room. You need a good sized solar panel to get any real usable power. Then you must worry about the other draw backs like what happens when it is dark. So, you pop a lithium battery in your device and now you’re back where you started.
Thermoelectric Generator
My personal favorite is powering devices from body heat. Thermoelectric generators convert temperature differences directly into electricity through a phenomenon called the seebeck effect. Unfortunately, I do not think they generate a lot of power but the idea of powering a device with your own body energy sounds very cool to me.
Supercapacitors
Supercapacitors could be used as a future battery. They fully charge almost instantly and as far as I know, they do not have the life span limitations of other batteries. I have used them in some of my Arduino projects to power little circuits. They seem to work well for small stuff. The downside is they do not hold as much power for their size. Maybe with advancements in nanotechnology, someone will solve that problem.
Biofuel Cells

There is also this new stretchable biofuel cells. They make electricity from sweat. Workout tracking devices could use something like this. But it would not be any good for the people that are not sweating.
Final thoughts

I do not think batteries will ever truly go away. There will always be a need to have energy storage. Most likely we will end up with some kind of hybrid devices that can pull energy from the environment around them and save that into some kind of power cells. I could see solar cells being on everyone’s phone if we can find a way to make them more efficient. Wireless chargers placed around buildings could be a cool idea. Phones batteries could get topped off as you walk by if we had something like that. But maybe if we are lucky someone like Tony Stark will find some magic element or combination of elements that will surpass lithium in every way.