What are these "last minute appeals" I read about in the news?

In criminal cases, a federal court may also review either a federal or state court conviction after all of the usual appeals have been exhausted. This is done by a petition for "habeas corpus" -- Latin for "you have the body." As stated in Brown v. Vasquez, “[t]he writ of habeas corpus is the fundamental instrument for safeguarding individual freedom against arbitrary and lawless state action.”

While only a tiny percentage of these petitions are granted, the reviews, especially in death penalty cases, have become highly controversial. Since an error in trying a death penalty case has extreme consequences, courts review them very scrupulously. 

Writs of Habeas Corpus can be filed for all serious criminal charges after every other type of appeal has been used. In addition, the Writ of Habeas Corpus can be filed in family law cases when a parent is denied custody of a child and in civil cases where a judge declares someone in contempt of court and threatens jail time. 

The Writ of Habeas Corpus, which is heard by the Supreme Court, is strictly policed to avoid excessive waste of time and tax dollars. In fact, most requests are denied by the court since they do not contain a federal issue that the Supreme Court can even review. Relief for a Habeas Corpus appeal is only granted where the defendant can show that an error of the trial court caused actual prejudice in their case. The Supreme Court does not have the actual ability to free the prisoner, either. In fact, if and when the Supreme Court finds that there was prejudice, the state court will decide whether the error affected the final judgment. If it in any way did, then they are obligated to release the prisoner.