Human ingenuity keeps finding more oil and gas but we are close to running out of IP addresses, at least in the old IPv4 system, which all of your are probably using right now. This does not mean the world will shut down - already, for example, all the computers in your home probably share a single IP address to the outside world, and for many of you that IP address is dynamically assigned by your Internet provider to further save addresses. Many web sites on the same server will share an IP address (which is actually a good reason not to used shared hosting, because if one of the other accounts on your server is a bad actor, your IP address can effectively get banned from sites and networks trying to ban that other person on your server).
However, a new system is in place, but as with many standards transitions the details are tricky. It will be interesting to see how this mostly free-market transition goes in comparison to government enforced transitions (e.g. television broadcast standards).
The following will probably just demonstrate my total ignorance of networking protocols, but I am not sure why IPv6 couldn't be written in a way that the extra bytes would just be ignored by IPv4 systems. It could be assumed that all IPv4 addresses of the form www.xxx.yyy.zzz map to www.xxx.yyy.zzz.000.000 in IPv6, but this may be wildly simplifying what is going on.
The reason I bring this us is because I have always thought the way black and white TV was transitioned to color was particularly clever. They could have broadcast color with three signals of Red, Green, and Blue levels, and then black and white TVs would have to be thrown out - they wouldn't show anything meaningful with that signal. Instead, though, they mapped color with a three part system of an absolute brightness signal for each pixel, plus two color signals. If you are familiar with Photoshop, when you choose a color, you can enter the color as three numbers R-G-B for the intensity of each color or as Hue-Saturation-Brightness. While not the same as the TV system, it is similar in that it has a pixel brightness component, plus to color components. (my memory is that in the TV system, it is brightness plus two colors and the third color -- blue, I think -- is arrived at by subtraction from the total brightness minus the two other colors.)
Here is the trick - the signal which was just the pixel brightness component is essentially identical to the old black and white TV signal -- after all, a black and white signal is just the relative brightness of each pixel. So they took a black and white signal and then added bandwidth so that there was more information if one had a color set. Both technologies, old and new, worked from the same signal.
I suppose the problem with this is that I am thinking of routers like telephones. Most folks know that if we dial more than 10 digits, the extras are just ignored. My guess is that routers are more finicky and precise than this, and they can't just ignore the fact the IP address they are getting are too long. But I still would imagine there could be a simple hardware hack to cheaply strip off the last part of a longer IP address so that older IPv4 infrastructure could still work in an IPv6 world. Or is this hopelessly misinformed and naive?