Gregg v. Georgia, Proffitt v. Florida, Jurek v. Texas, Woodson v. North Carolina, and Roberts v. Louisiana, 428 U.S. 153 (1976), is a landmark decision of the United States Supreme Court. It reaffirmed the Court's acceptance of the use of the death penalty in the United States, upholding, in particular, the death sentence imposed on Troy Leon Gregg. The set of cases is referred to by a leading scholar as the July 2 Cases, and elsewhere referred to by the lead case Gregg. The court set forth the two main features that capital sentencing procedures must employ in order to comply with the Eighth Amendment ban on "cruel and unusual punishments". The decision essentially ended the de facto moratorium on the death penalty imposed by the Court in its 1972 decision in Furman v. Georgia (1972). Justice Brennan's dissent famously argued that "The calculated killing of a human being by the State involves, by its very nature, a denial of the executed person's humanity [...] An executed person has indeed 'lost the right to have rights.'"

All five cases share the same basic procedural history. After the Furman decision, the states of Georgia, Florida, Texas, North Carolina, and Louisiana amended their death penalty statutes to meet the Furman guidelines. Subsequently, the five named defendants were convicted of murder and sentenced to death in their respective states. The respective state supreme courts upheld the death sentence. The defendants then asked the U.S. Supreme Court to review their death sentence, asking the Court to go beyond Furman and declare once and for all the death penalty to be "cruel and unusual punishment" and thus in violation of the Constitution; the Court agreed to hear the cases.

In the July 2 Cases, the Court's goal was to provide guidance to states in the wake of Furman. In Furman only one basic idea could command a majority vote of the Justices: capital punishment, as then practiced in the United States, was cruel and unusual punishment because there were no rational standards that determined when it was imposed and when it was not. The question the Court resolved in these cases was not whether the death sentence imposed on each of the individual defendants was cruel, but rather whether the process by which those sentences were imposed was rational and objectively reviewable.

The defendants in each of the five cases urged the Court to go further than it had in Furman by holding once and for all that capital punishment was cruel and unusual punishment that violated the Eighth Amendment. However the Court responded that "The most marked indication of society's endorsement of the death penalty for murder is the legislative response to Furman." Both Congress and 35 states had complied with the Court's dictates in Furman by either specifying factors to be weighed and procedures to be followed when imposing a death sentence, or dictating that the death penalty would be mandatory for specific crimes. Furthermore, a referendum in California had overturned the California Supreme Court's earlier decision (California v. Anderson) holding that the death penalty violated the California constitution. The fact that juries remained willing to impose the death penalty also contributed to the Court's conclusion that American society did not believe in 1976 that the death penalty was unconstitutional.

The Court also found that the death penalty "comports with the basic concept of human dignity at the core of the [Eighth] Amendment". The death penalty serves two principal social purposes—retribution and deterrence. "In part, capital punishment is an expression of society's moral outrage at particularly offensive conduct". But this outrage must be expressed in an ordered fashion, for America is a society of laws. Retribution is consistent with human dignity, because society believes that "certain crimes are themselves so grievous an affront to humanity that the only adequate response may be the penalty of death". And although it is difficult to determine statistically how much crime the death penalty actually deters, the Court found that in 1976 there was "no convincing empirical evidence" supporting either the view that the death penalty is an effective deterrent to crime or the opposite view. Still, the Court could not completely discount the possibility that for certain "carefully contemplated murderers", "the possible penalty of death may well enter into the cold calculus that precedes the decision to act".

Finally, the Court considered whether the death penalty is "disproportionate in relation to the crime for which it is imposed". Although death is severe and irrevocable, the Court could not say that death was always disproportionate to the crime of deliberately taking human life. "It is an extreme sanction, suitable to the most extreme of crimes."

The Court was determined to simultaneously save capital punishment in the United States and impose some reasoned basis for carrying it out. That reasoning flows from the Eighth Amendment's cruel and unusual punishment clause. Although capital punishment, per se, was not found by the Court to be cruel and unusual, it must still be carried out in a manner consistent with the evolving standards of decency that mark the progress of a maturing society. In the Court's view, the country's history with capital punishment suggests that those evolving standards of decency could not tolerate a return to the mandatory death penalty for murder that had prevailed in medieval England.^{[citation needed]}

In 18th century Britain, the penalty for a vast number of serious crimes, including murder, was death. This rule traveled with the colonists to America, and was the law in all states at the time the Eighth Amendment was adopted in 1791. By then, however, a problem with the common-law mandatory death penalty had crept into the legal system. If the jury has only two options—convicting a defendant of murder, where the penalty is death, or acquitting the defendant outright—it has no vehicle to express the sentiment that the defendant should be punished somehow, but not executed. Faced with this dilemma, some juries would acquit the defendant in order to spare his life. Of course, this meant that an obviously guilty person would go free.^{[citation needed]}