Supposedly the world is nearly out of IP Adresses for IPv4(what nearly every computer or device uses. Then what? Well Its not really known what happens next. For more check this out. You wont immediately be unable to connect the day they run out due to the fact your ISP most likely has many IP addresses reserved for new devices, but when those run out it could be a dark day for the internet. The main problem is the lack of support for IPv6 which as said in the article has been around since windows 98. It uses 128 bit addresses which are much longer and thus have more combinations (IPv4 are 32 bit)
I personally think this is going to be very very very bad. I think it needs to be much bigger of a concern than it currently is right now.