The Constitution does not guarantee a convicted offender a right of appeal, but every jurisdiction allows at least one appeal as a right, and many states have two levels of appellate courts and two levels of appeals. For some second level appeals, the court has the discretion to hear only those cases that it chooses. Because of the guarantee against double jeopardy, the prosecution may not appeal a not-guilty verdict. Thus, an acquittal stands, even if it was based upon an egregious mistake by the judge in interpreting the law or upon an incomprehensible factual finding by the judge or jury.

After an offender's state court appeals have been exhausted, he/she may file a habeas corpus petition in federal district (trial level) court alleging that he/she is being held in state custody in violation of his/her federally guaranteed statutory or constitutional rights. (Federal prisoners may also petition the federal courts for post-conviction relief in the event, for example, that new evidence which could not have been discovered before trial, demonstrates innocence.) The right of habeas corpus is guaranteed by the Constitution and implemented by a federal statute. In some limited circumstances, an offender who was unsuccessful in the first habeas corpus proceeding may bring additional habeas corpus petitions alleging other constitutional violations, thus initiating the whole process anew.