Space Warfare?

So you hear about spy satelittes being up in space. US spy satts above Chinese airspace and vice versa. Since no one had jurisdiction over space, what stops China have blowing up US spy sats and vice versa?

>>1
but being Northern Virginia, they built apartments on the woods behind the school! So what's left? Yup. (I live about a mile from there, actually graduated from there back in 1995...it's apparently a hellhole now, with more ridiculously strict rules than usual.)