The US has fought some interesting cases that have extended US law outside of the United States and cases that allow foreign nationals to use US law outside of the United States. A good example of the latter is when Iraqi citizens were able to sue Blackwater in a US court or where asylum seekers were able to sue governments and cartel members in a US court.

The way I see it, as a largely uneducated-about-the-formalities-of-law citizen, is that this exemplifies the need for a world court who has proper interests and jurisdiction to hold fair trials for international matters.