Writs of Certiorari. Parties who are not satisfied with the decision of a lower court must petition the U.S. Supreme Court to hear their case. The primary means to petition the court for review is to ask it to grant a writ of certiorari. ... The Supreme Court has its own set of rules.
Supreme Court Procedures | United States Courts
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Supreme Court Procedures

Writs of Certiorari
Parties who are not satisfied with the decision of a lower court must petition the U.S. Supreme Court to hear their case. The primary means to petition the court for review is to ask it to grant a writ of certiorari. This is a request that the Supreme Court order a lower court to send up the record of the case for review. The Court usually is not under any obligation to hear these cases, and it usually only does so if the case could have national significance, might harmonize conflicting decisions in the federal Circuit courts, and/or could have precedential value. In fact, the Court accepts 100-150 of the more than 7,000 cases that it is asked to review each year. Typically, the Court hears cases that have been decided in either an appropriate U.S. Court of Appeals or the highest Court in a given state (if the state court decided a Constitutional issue).