Every few months, the people who know the most about the Internet's architecture warn us that the Internet is doomed — address space is running out and we need to change to IPv6 as fast as we can. And other people call them Chicken Littles.
The best case for the version that says the sky is in fact going to fall isn't simply IPv4 number address space even though there's problems there — we keep inventing fixes of various degrees of ugliness that stave off the day of reckoning for that one, and there are huge allocated but unused blocks that could in theory be repurposed. No, The Internet's real Achilles Heel may be routers.
Router mapping tables keep growing, and there are signs that (despite clever enhancements) the BGP tables are getting up to capacity. And, we now hear the cost of routing all the traffic may be growing too quickly. Which means we may soon all be singing The Day The Routers Died: