A litigant who files an appeal, known as an "appellant," must show that the trial court made a legal error that affected the decision in the case. The court of appeals makes its decision based on the record of the case established by the trial court. It does not receive additional evidence or hear witnesses. The court of appeals may also review the factual findings of the trial court, but will typically only overturn a decision on factual grounds if the findings were "clearly erroneous."

The court of appeals decision usually will be the last word in a case, unless it sends the case back to the trial court for additional proceedings, or the parties ask the U.S. Supreme Court to review the case. Appeals are decided by panels of three judges working together. The appellant presents legal arguments to the panel, in writing, in a document called a "brief." In the brief, the appellant tries to persuade the judges that the trial court made an error, and that its decision should be reversed. On the other hand, the party defending against the appeal, known as the "appellee," tries in its brief to show why the trial court decision was correct, or why any error made by the trial court was not significant enough to affect the outcome of the case.

Although some cases are decided on the basis of written briefs alone, many cases are selected for an "oral argument" before the court. Oral argument in the court of appeals is a structured discussion between the appellate lawyers and the panel of judges focusing on the legal principles in dispute. Each side is given a short time — usually about 15 minutes — to present arguments to the court.

A litigant who loses in a federal court of appeals, or in the highest court of a state, may file a petition for a "writ of certiorari," which is a document asking the Supreme Court to review the case. The Supreme Court, however, does not have to grant review. The Court will typically agree to hear a case only when it involves an unusually important legal principle, or when two or more federal appellate courts have interpreted a law differently. There are also a small number of special circumstances in which the Supreme Court is required by law to hear an appeal. When the Supreme Court hears a case, the parties are required to file written briefs and the Court may hear oral argument.