Certiorari is most commonly associated with the writ that the Supreme Court of the United States issues to review a lower court's judgment.   A case cannot, as a matter of right, be appealed to the U.S. Supreme Court; therefore, a party seeking to appeal from a lower court decision may file a petition to a higher court for a writ of certiorari. That writ is the formal order to the lower court to deliver its record of the case for review.  

In the US Supreme Court, if four Justices agree to review the case, then the Court grants certiorari (often abbreviated as "cert."); if that does not happen, the Court denies certiorari.  Most of the Justices participate in a "cert pool," meaning their law clerks collectively assign out among themselves the various petitions for certiorari (known commonly as "cert petitions") and prepare memoranda for the Justices summarizing the issues and recommending whether or not the Court should grant certiorari.  Critics of this process note the shrinking number of cases the Court has agreed to hear in recent years, theorizing that the "cert pool" tends to increase the number of recommended denials.   

 Rule 10 of the Supreme Court Rules lists the criteria for granting certiorari and explains that the decision to grant or deny certiorari is discretionary.  A decision to deny certiorari does not necessarily imply that the higher court agrees with the lower court's ruling; instead, it simply means that fewer than four justices determined that the circumstances of the decision of the lower court warrant a review by the Supreme Court.  The Court's orders granting or denying certiorari are issued as simple statements of actions taken, without any explanations given for denial.  It has been suggested that the Court should indicate its reasons for denial.  In Maryland v. Baltimore Radio Show, Inc., however, the Court explained that because of practical considerations (to allow the Court to carry out its indispensable duties), Congress has allowed the control of the Court's business to remain within the Court's discretion.

Originally, the writ of certiorari was a proceeding through which a superior court required a lower court to submit the full record of a case for review.  In fact, the term comes from Law Latin, meaning "to be more fully informed." Under the current rules and practice of the Supreme Court, however, key elements of the proceedings below are submitted along with a petition for certiorari. (See Supreme Court Rules, Rule 14.) And in some states the old terminology has been replaced. In Arizona, for example, relief formerly obtained by the writs of prohibition, mandamus and certiorari is now obtained through a "special action."  Many state appellate courts, however, still used the term to describe the formal instrument by which they accept review of cases from their lower courts.