How has the Supreme Court applied the Eighth Amendment to cases involving capital punishment?

The Supreme Court has applied the Eighth Amendment, which prohibits cruel and unusual punishment, to capital punishment cases by establishing legal standards that govern the death penalty's implementation. Key rulings, such as Furman v. Georgia (1972), highlighted the arbitrary nature of capital sentencing, leading to a temporary halt on the death penalty. Subsequent cases, like Gregg v. Georgia (1976), upheld the constitutionality of the death penalty but mandated that states adopt specific procedural safeguards to ensure fairness. Additionally, the Court has ruled against executing individuals who are intellectually disabled or minors, emphasizing evolving standards of decency in society.