I hear all the time about how US Troops arrested so-and-so in Iraq...

Under what powers comes their authority for "arrest"?

Can't be US Law because US Law (which includes USMCJ) is not applicable over there. Except for our soldiers...

Can't be UN or NATO because our action wasn't sanctioned by those authorities.

Can't be Iraqi Law since their laws are pretty much moot and were suited for a dictatorial regime.

Would it be International Law? Are there International Laws of War? When were they written?

I'm thinking maybe Martial Law. The went in, drove out the ruling Bathe Party. Then declared themselves to be the Law in Iraq.