Olympic Help

Maybe somebody on here can help me out with something. I was flipping to the opening ceremonies of the Olympics during commercials of the Eagles game and I noticed something peculiar. Puerto Rico has a national team. Now, I have noticed this before and have never understood it. Puerto Rico is owned by the U.S. I believe that they can vote and everything. No passport is needed to travel there. Why are they here? They are pretty much the 51st state. I don't get it. They are not their own country. There were also other examples of this where little nothing islands that are part of a larger country sent competitors. Why? If someone would please explain this to me I would greatly appreciate it.

Also, why the hell is Iraq allowed in. They were banned and now they are not? Bullshit.

P.S.- The U.S. Olympic team looked awfully gay in their sportcoats and old man hats. Just throwing that out there.