If you are convicted by a trial you have the right to appeal your case to the Court of Appeals in the circuit in which your district court resides. There are eleven circuit courts of appeal not including the District of Columbia which is its own circuit court.
Taking an appeal is an important step in challenging pretrial, trial, and post-trial matters that were raised by your attorney through pretrial pleadings, trial and sentencing objections, and sentencing mitigation memorandums. An appeal can overturn a conviction or the sentence. This is an important step you should exercise in all cases where you went to trial or did not waive your appeal rights.
If the appeal is not successful, you have the right to go to the Supreme Court within 90 days of the applicable appellate court decision. Challenging a case in the Supreme Court is difficult and requires a unique question of law that the justices could consider and could affect other defendants throughout the criminal justice system.
Finally, if none of this works, there is always the habeas corpus petition pursuant to 28 U.S.C. 2255 which attacks your conviction and sentence pursuant to ineffective assistance of counsel claims. Ineffective assistance of counsel claims must include not only that your attorney made an error but that the error changed the outcome of your case and but for that error, a different decision would have been made by the court. See Strickland v. Washington.