Does an iphone (bought in USA) works in europa with another provider?

In the Netherlands the iPhone 4s 32GB are like 700 dollar. In USA I can buy them for much less. But if i bought one in USA and bring it to the Netherlands and use it there with an dutch provider, does the iphone still work correctly?

I know some phones are sim locked, and I can normally unlock them in the Netherlands for around 10 euro. But are there other things that need to know?

I'm not shure but i heard at & t uses the same coding as japan so its more universal but i don't know lol.