Only Congress can declare war against another nation. Unless Congress has declared war, the president has limited engagement powers, and must report actions and justification to Congress within (I believe 90 days). Any further action must be approved by Congress.
In a wartime stance, action should be taken by the commander on the scene unless it is negated by a higher command. Otherwise, any action taken must be approved by a higher command. Since the US is not in a declared war, all actions must be approved by a higher command (Top down) and are usually approved by POTUS. This is why it is imperative that Congress declare war on ISIS. This would allow the commanders in the field to take action without clearing every shot with Washington.