T H I S chapter is devoted to 125 of the Supreme Court cases decided after capital punishment was reinstated in 1976. Since then, the Court has been engaging in a time-consuming effort to fine tune the way capital punishment is applied. According to law professor Franklin Zimring, in the century before Furman, the Supreme Court “only rarely reviewed state death sentences,” but in the two decades after 1976, “the substantive law and procedure in state death penalty cases became the most frequent business of that court.”1 Some of the issues have been so controversial that the Court has changed positions on them several times. The cases address nine basic and, frequently, interrelated issues: (1) the constitutionality of death penalty statutes, (2) what crimes are capital, (3) mitigating circumstances, (4) aggravating circumstances, (5) the appellate process, (6) capital juries, (7) who may or may not be executed, (8) assistance of counsel, and (9) other procedural issues. Many of the cases addressed multiple issues, but generally only the most important issue is examined. For the most part, cases in each subsection are presented in chronological order and, for many of the cases, only brief descriptions of the Court’s holdings are provided. For other cases, case descriptions are more detailed.2 Tables at the end of each section list the cases in that section, along with an identifying term, in chronological order.