There are many types of appeals for immigration cases. Where an appeal must be filed depends on which department or agency issued the denial. For instance, with deportation/removal cases, a denial of an Immigration Judge can be appealed to the Board of Immigration Appeals. A decision from the Board of Immigration Appeals can be appealed to the Federal Court of Appeal in the appropriate circuit.
Depending on where a criminal relief case originates (state or federal), the case can be appealed from the trial court to the appellate court and ultimately either the State Supreme Court (if it is a state case) and U.S. Supreme Court (if it is a federal case).
Because appeals have various procedures and strict deadlines, it is important to retain a qualified immigration attorney to make sure that the appeal is filed correctly.