The Supreme Court has the power of judicial review, which allows it to to rule on whether laws are unconstitutional.  It also interprets the U.S. Constitution and the nation's laws and makes sure they are applied correctly.  The cases it hears include ones involving the Constitution, federal laws, treaties, and disputes between states.  All of these powers are derived from the Constitution.  Lastly, according to the Rule of Four, if four justices decide the case is worthy of a trial, the Supreme Court will hear it.