When the US Supreme Court agrees to hear a case, it issues a legal order called a "writ of certiorari" telling the lower court to send up the case files.
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The Court grants certiorari to the petitioner, and issues a writ of certiorari to the lower court, asking for the case files.
Nothing unless a case appealed to the Supreme Court asks a constitutional question directly related to that law. If the Court grants certiorari on such a case, they can use the power of judicial review to decide whether the law conforms with the US Constitution. If they determine the law is unconstitutional, they can nullify it and render it unenforceable.The Supreme Court can only apply judicial review to legislation under review in a case on appeal. Contrary to popular belief, the Supreme Court cannot be proactive in reviewing laws.The justices don't have constitutional authority to overturn legislation simply because they don't like it. Someone who is severely and directly, negatively affected by the law, and has a grievance that can be resolved by a court, must file suit and exhaust the required appeals process before the Supreme Court would have an opportunity to review the case (and the law).
The case must be unique and important in order for the Supreme Court to accept the case. The case can also be accepted if it is to resolve a conflict of law.
The power of the supreme court to declare a law "unconstitutional" is called Judicial Review. No part of the constitution actually grants this power explicitly to the Supreme Court, but the case of Marbury vs. Madison established this power and has been the accepted precedent for granting the Supreme Court the power of Judicial Review ever since.
From the case of Marbury v. Madison