Do they ever mention what other parts of the world are like? I think it would be interesting to see how citizens of Europe and Asia have survived if they did at all. I am sure they would have had some sort of vault network as well.

I don't believe so. China's probably in the same ship as the US; vestiges of it's government trying to claw back power from local warlords, tribes, and new states. I believe there was a planned but (thankfully) scrapped addition to the series in which the player would've travelled west, passing into the remains of the USSR and a newly Imperial China.

Europe and the Middle East were already battered and broken by the time of the Great War, so they can't have faired too well. They each had their own nuclear arsenal, too, making them prime targets (particularly for each other) in the exchanges. Lacking wealthy, stable, or powerful governments, something like the Vault program pobably wouldn't have taken place. At least not on the same scale. I'd expect to find both areas populated largely by ghouls, with tribal chieftains holding every hill top, and one or two "Enclavesque" pockets of civilisation at the fringes. There's clearly some sophistication, as neither "What Ho, Old Boy" Tenpenny nor "Oim Feckin' Oirish" Moriaghty were particularly backward, and they both had the means to cross an irradiated, mutant-fish infested ocean. But then they were pretty dismal character concepts, so I think it'd be best to just ignore their inclusion all together.

Edit: Jesus.. 2 years ago? Appologies for the necro, I followed a link here and didn't spot the date.