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It's more of a cold war because the assets are being put in place but they aren't being used in anger. There are satellites taking pictures of other satellites. There are anti-satellite missiles. Satellite capture/grappling mechanisms are being tested. We don't know what the X-37B is doing but it could capture small satellites and return them to Earth. Orbital drop pods and orbit-to-ground missiles are being developed. This is all unclassified so there could be more.