Final answer:
Court rulings against capital punishment typically involve the Eighth Amendment, which bans cruel and unusual punishments. This has led to limitations on the death penalty, such as prohibitions on executing juveniles, those with intellectual disabilities, and for non-murder crimes.
Step-by-step explanation:
Court rulings against the use of capital punishment generally involve the Eighth Amendment of the U.S. Constitution. This amendment includes a ban on 'cruel and unusual punishments' which has been the basis for various Supreme Court decisions regarding the death penalty. For example, Furman v. Georgia ruled that the inconsistent imposition of the death penalty was unconstitutional. While the Supreme Court has found capital punishment constitutional in certain contexts, it has also set limits, such as ruling that executions of those with intellectual disabilities (Atkins v. Virginia), juveniles (Roper v. Simmons), or for crimes not involving murder or against the state (Kennedy v. Louisiana) are cruel and unusual.