>And who takes its place?

Anybody who can (EU, Yuan) does not want to. Primairly because as export based economies, they want a weak currency in relation to a strong reserve (dollar) so they can make their goods more competitive, and also because surplus naturally appreciates a currency without central bank intervention via buying US treasuries to offset the appreciation. And for China, they're not going to accept the liberalized capital controls neede for it either.

So the answer is if the US dollars fail it would be global economic collapse and then chaos, but contrary to the rhetoric the rest of the world's economic systems are too uniquely vested in the USD to see it fail. As for gold, well we come to the same problem as noted above but worse, and in that situation the US actually holds the highest gold reserves so they still benefit the most out of it.