https://supreme.justia.com/stages-of...y%20of%20cases.
Writ of Certiorari
There is no absolute right to have the Court hear an appeal. Someone who wants to appeal to the Court must file a petition for a writ of certiorari. The Justices will receive briefs and potentially amicus briefs on whether the writ should be granted. They then will decide at a conference whether to grant the writ. (Briefs, amicus briefs, and conferences play a larger role later in the case and are discussed in more detail below.) This decision does not require a majority. Only four of the nine Justices must agree to grant a writ of certiorari. This tells the lower court to prepare the record for review by the Supreme Court, and the case is placed on the Supreme Court docket.
If the Court denies a writ of certiorari, the decision of the lower court stands, and the case ends. This happens in the overwhelming majority of cases. Only a tiny fraction of these petitions are successful. The Court may be more likely to grant a writ of certiorari if lower courts have reached clashing decisions on the issue, or if it has broad national significance. Granting a writ of certiorari does not necessarily mean that the Court thinks that the lower court was wrong. However, the Court recently has reversed much more often than it has affirmed.
