Criminal convictions in a state court can be appealed through the state appellate court or court of appeals. Federal convictions can be appealed through the federal court of appeals. To appeal the decision of a district court, a petition must be filed with the court of appeals within a certain time period. This petition should include all the facts necessary to understand the case, the question that's being asked the court, and a description of the relief being sought. Generally, the grounds for an appeal are based on the claim that the judge in the lower court made a legal mistake, which led to the conviction. If this is found to be the case, the appellate court is empowered to reverse the decision of the lower court. Appeal cases are generally heard once only by the appellate court, although you can sometimes obtain a rehearing by the appellate court following a petition to that court. Cases can also be appealed to the state supreme courts, which first review cases to decide whether they'll accept the appeal and try the case. All cases can be appealed to the U.S. Supreme Court if the grounds for the appeal are that the conviction was unconstitutional. The U.S. Supreme Court first reviews cases to decide whether or not they fall within their jurisdiction. If you've been convicted of a crime and wish to petition for an appeal, you should consider consulting an attorney.