Final answer:
Appeals related to the death penalty are heard by higher courts in the U.S., such as special appellate courts or the state supreme courts, with ultimate authority resting in the U.S. Supreme Court. The International Court of Justice does not have jurisdiction over these appeals.
Step-by-step explanation:
The jurisdiction for hearing appeals related to the death penalty typically lies with higher courts in the United States judicial system. Once a trial court with general jurisdiction has handed down a sentence, appeals can be made by the defense or prosecution to a special appellate court or the state supreme court.
In landmark cases such as Furman v. Georgia, the Supreme Court of the United States ruled on the constitutionality of the death penalty, emphasizing the prohibition of cruel and unusual punishment under the Eighth and Fourteenth Amendments.
The Supreme Court has also set significant limits on the death penalty, as seen in Kennedy v. Louisiana where the death penalty was deemed unconstitutional for non-homicide crimes. In cases involving intellectual disabilities, the Supreme Court has ruled against execution, as per Atkins v. Virginia.
However, it's important to note that in Breard v. Greene, the International Court of Justice was found not to have jurisdiction in capital punishment cases involving foreign nationals. Therefore, death penalty appeals within the U.S. are managed by the domestic criminal justice system with final authority resting in the U.S. Supreme Court.