Supreme Court cases come in three varieties. Least numerous are the "original jurisdiction" actions, brought by one state against another, or between states and the federal government. The Constitution also empowers the Court to hear "all Cases affecting Ambassadors, other public Ministers and Consuls." In these the Court sits as a trial body from which there is no appeal.

Few original jurisdiction cases are filed—usually one to five a term—but sheer bulk makes many of these difficult. In 1952 Arizona sued California over water from the Colorado River. The completed trial record covered more than 26,000 pages. Briefs and other documents filed by the states took 4,000 more. The Justices heard 16 hours of oral argument in the fall of 1961, six hours more in November, 1962. Arizona prevailed in the Court’s decision in 1963.

More numerous, but mercifully shorter, are cases from state courts. If any state tribunal decides a federal question and the litigant has no further remedy within the state, the Supreme Court may consider it.

Most common—roughly two-thirds of the total—are requests for review of decisions of federal appellate or district courts. The great majority of cases reach the Supreme Court through its granting of petitions for writs of certiorari, from the Latin certiorari volumnus, "we wish to be informed."

Normally the "writ of cert" says in effect to an appellate court, "Send us the record in this case you decided recently." In very rare instances a writ of certiorari before appellate judgment says, " Send us the record in this case you haven’t reviewed yet." It enables the Court to act with maximum speed in unusual cases of great public importance.

With some 7,000 petitions annually, deciding which case to decide is a load in itself. According to a court historian, "it is arguably the most important stage in the entire Supreme Court process." In the 1999-2000 Term the Court heard argument on 83 cases and decided 74 cases. Four more cases were subsequently remanded or dismissed. In addition, 50 cases were decided summarily, that is, without argument.

Each Justice determines how he or she will vote to accept or reject each certiorari petition, usually calling for a law clerk’s memorandum analyzing the petition. Eight of the Justices make use of a "cert pool" system. As the certiorari petitions are received, their clerks take turns writing memorandums, and each Justice conducts whatever additional research is necessary. Justice Stevens prefers to rely on his own clerks, and all the Justices review all petitions.

Roughly 70 percent of the petitions end at this point, with a vote not to accept the case. The Justices may be satisfied that the decision of the lower court was correct, or that the case has no national significance, or, in some instances, that the Supreme Court lacks jurisdiction. Whatever the reason for denial, the effect is to allow the decision of the lower court to stand.