In the 1960s, the NAACP Legal Defense Fund, led by Professor Anthony Amsterdam mounted a full-scale attack on the death penalty.  Adopting a "moratorium strategy," the LDF succeeded in blocking all executions for five years, creating a "death-row logjam."

In Furman v Georgia in 1972, the Court voted 5 to 4 to invalidate all then-existing death penalty laws based on the inherent arbitrariness of their application.  In a key concurring opinion, justices said the randomness of being executed in the United States compared to "being struck by lightening." Most observers at the time concluded that there would never again be an execution in the United States.  They were wrong.  In 1976, in Gregg v. Georgia, the Court upheld Georgia's new capital-sentencing procedures, concluding that they had sufficiently reduced the problem of arbitrary and capricious imposition of death associated with earlier statutes.  The law upheld in Gregg, which provided for bifurcated proceedings, one to determine guilt and one to determine whether to execute, has since become the model for statutes in death penalty states.  In the death penalty phase of trials, jurors are now required to make specific findings concerning the presence or absence of mitigating and aggravating factors concerning the defendant's crime.

The Court continued to face questions concerning the appliction of the death penalty: to non-murderers, to minors, to mentally disabled prisoners, to racial minorities.  One such case is McCleskey v. Kemp (1987), a challenge based on a study that showed murderers of white victims were far more likely to be sentenced to death than murderers of black victims.

The Court continues to address the constitutionality of the death penalty in special contexts.  In 2002, the Supreme Court held in Atkins v Virginia that  the death penalty was unconstitutional when applied to the mentally retarded.  Voting 6 to 3, the Court concluded that executions of the mentally retarded offended the "evolving standards of decency" test laid out in previous cases for evaluating the constitutionality of criminal punishments.  The same test was applied in 2005 in Roper v Simmons to find that the death penalty could not be applied to persons under the age of 18 at the time of their crime.  Justice Kennedy, for the 5 to 4 Court, wrote that "it is fair to say that the United States now stands alone in a world that has turned its face against the juvenile death penalty." Roper reversed a decision of the Court sixteen years earlier upholding such sentences.