Some of the commentary I've read on the recent Hamden decision revolves around the premise that the Supreme Court didn't have jurisdiction to hear the case, because of the plain language of the law by which the president was detaining the prisoners.
The prisoners were being held per the Geneva Conventions (among other reasons), and the Geneva Conventions were part of a treaty/agreement that the United States entered into.
Why does this matter? Well, I didn't catch it, myself (I'm merely a student, bear with me), but Dr. Stephen Taylor at PoliBlog noted that perhaps this little phrase in the Constitution, in Article VI (the Supremacy Clause), might matter:
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
See, the agreements were made under the Authority of the United States, which subjects them to Constitutional review, and the Constitution is interpreted by the Court, not the president or Congress.