(1) Brumfield v. Cain: By a vote of 5-4 the judgment of the Fifth Circuit is vacated and the case is remanded.  Per Justice Sotomayor's opinion for the Court: "In Atkins v. Virginia, 536 U. S. 304 (2002), this Court recognized that the execution of the intellectually disabled contravenes the Eighth Amendment’s prohibition on cruel and unusual punishment. After Atkins was decided, petitioner, a Louisiana death-row inmate, requested an opportunity to prove he was intellectually disabled in state court. Without affording him an evidentiary hearing or granting him time or funding to secure expert evidence, the state court rejected petitioner’s claim. That decision, we hold, was “based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U. S. C. §2254(d)(2). Petitioner was therefore entitled to have his Atkins claim considered on the merits in federal court.

Justice Sotomayor's majority opinion was joined by Justices Kennedy, Ginsburg, Breyer, and Kagan. Justice Thomas dissented, joined except as to Part I-C by the Chief Justice and Justices Scalia and Alito. Justice Alito also dissented separately, joined by the Chief Justice.

(2) Ohio v. Clark:  By a vote of 9-0 the judgment of the Ohio Supreme Court is reversed and the case is remanded.  Per Justice Alito's opinion for the Court: "Darius Clark sent his girlfriend hundreds of miles away to engage in prostitution and agreed to care for her two young children while she was out of town. A day later, teachers discovered red marks on her 3-year-old son, and the boy identified Clark as his abuser. The question in this case is whether the Sixth Amendment’s Confrontation Clause prohibited prosecutors from introducing those statements when the child was not available to be crossexamined. Because neither the child nor his teachers had the primary purpose of assisting in Clark’s prosecution, the child’s statements do not implicate the Confrontation Clause and therefore were admissible at trial."

Justice Alito's majority opinion was joined by the Chief Justice and Justices Kennedy, Breyer, Sotomayor, and Kagan. Justice Scalia filed an opinion concurring in the judgment, joined by Justice Ginsburg.  Justice Thomas also filed an opinion concurring in the judgment.

(3) Davis. v. Ayala: By a vote of 5-4 the judgment of the Ninth Circuit is reversed and the case remanded.  Per Justice Alito's opinion for the Court: "A quarter-century after a California jury convicted Hector Ayala of triple murder and sentenced him to death, the Court of Appeals for the Ninth Circuit granted Ayala’s application for a writ of habeas corpus and ordered the State to retry or release him. The Ninth Circuit’s decision was based on the procedure used by the trial judge in ruling on Ayala’s objections under Batson v. Kentucky, 476 U. S. 79 (1986), to some of the prosecution’s peremptory challenges of prospective jurors. The trial judge allowed the prosecutor to explain the basis for those strikes outside the presence of the defense so as not to disclose trial strategy. On direct appeal, the California Supreme Court found that if this procedure violated any federal constitutional right, the error was harmless beyond a reasonable doubt. The Ninth Circuit, however, held that the error was harmful. The Ninth Circuit’s decision was based on the misapplication of basic rules regarding harmless error. Assuming without deciding that a federal constitutional error occurred, the error was harmless under Brecht v. Abrahamson, 507 U. S. 619 (1993), and the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), 28 U. S. C. §2254(d).

Justice Alito's majority opinion was joined by the Chief Justice and Justices Scalia, Kennedy, and Thomas. Justices Kennedy and Thomas also filed concurring opinions. Justice Sotomayor dissented, joined by Justices Ginsburg, Breyer, and Kagan.

(4) Walker v. Texas Division, Sons of Confederate Veterans, Inc.: By a vote of 5-4 the judgment of the Fifth Circuit is reversed.  Per Justice Breyer's opinion for the Court: "Texas offers automobile owners a choice between ordinary and specialty license plates. Those who want the State to issue a particular specialty plate may propose a plate design, comprising a slogan, a graphic, or (most commonly) both. If the Texas Department of Motor Vehicles Board approves the design, the State will make it available for display on vehicles registered in Texas. In this case, the Texas Division of the Sons of Confederate Veterans proposed a specialty license plate design featuring a Confederate battle flag. The Board rejected the proposal. We must decide whether that rejection violated the Constitution’s free speech guarantees....We conclude that it did not....we hold that Texas’s specialty license plate designs constitute government speech and that Texas was consequently entitled to refuse to issue plates featuring SCV’s proposed design."

Justice Breyer's majority opinion was joined by Justices Thomas, Ginsburg, Sotomayor, and Kagan.  Justice Alito dissented, joined by the Chief Justice and Justices Scalia and Kennedy.

(5) McFadden v. United States: By a vote of 9-0 the judgment of the Fourth Circuit is vacated and the case is remanded. Per Justice Thomas's opinion for the Court: "The Controlled Substance Analogue Enforcement Act of 1986 (Analogue Act) identifies a category of substances substantially similar to those listed on the federal controlled substance schedules, 21 U. S. C. §802(32)(A), and then instructs courts to treat those analogues, if intended for human consumption, as controlled substances listed on schedule I for purposes of federal law, §813. The Controlled Substances Act (CSA) in turn makes it unlawful knowingly to manufacture, distribute, or possess with intent to distribute controlled substances. §841(a)(1). The question presented in this case concerns the knowledge necessary for conviction under §841(a)(1) when the controlled substance at issue is in fact an analogue. We hold that §841(a)(1) requires the Government to establish that the defendant knew he was dealing with “a controlled substance.” When the substance is an analogue, that knowledge requirement is met if the defendant knew that the substance was controlled under the CSA or the Analogue Act, even if he did not know its identity. The knowledge requirement is also met if the defendant knew the specific features of the substance that make it a “‘controlled substance analogue.’” §802(32)(A). Because the U. S. Court of Appeals for the Fourth Circuit approved a jury instruction that did not accurately convey this knowledge requirement, we vacate its judgment and remand for that court to determine whether the error was harmless."

Justice Thomas's majority opinion was joined in full by all other justices except the Chief Justice, who filed an opinion concurring in part and concurring in the judgment.

(6) Reed v. Town of Gilbert: By a vote of 9-0 the judgment of the Ninth Circuit is vacated and the case is remanded. Per Justice Thomas's opinion for the Court: "The town of Gilbert, Arizona (or Town), has adopted a comprehensive code governing the manner in which people may display outdoor signs. Gilbert, Ariz., Land Development Code (Sign Code or Code), ch. 1, §4.402 (2005). The Sign Code identifies various categories of signs based on the type of information they convey, then subjects each category to different restrictions. One of the categories is “Temporary Directional Signs Relating to a Qualifying Event,” loosely defined as signs directing the public to a meeting of a nonprofit group. §4.402(P). The Code imposes more stringent restrictions on these signs than it does on signs conveying other messages. We hold that these provisions are content-based regulations of speech that cannot survive strict scrutiny."

Justice Thomas's majority opinion was joined by the Chief Justice and Justices Scalia, Kennedy, Alito, and Sotomayor. Justice Alito filed a concurring opinion, joined by Justices Kennedy and Sotomayor.  Justice Breyer filed an opinion concurring in the judgment.  Justice Kagan also filed an opinion concurring in the judgment, joined by Justices Ginsburg and Breyer.