Appellate court - a court which hears cases which have been decided in lower courts. For cases involving state law, most states provide state appellate courts, while federal circuit courts ("courts of appeal") deal with most appeals related to federal law. The State Supreme Court is the highest appellate court, the "court of last resort," for cases involving state law, while the US Supreme Court is the highest appellate court, the "court of last resort," for cases involving federal law.