Badgerow sought to vacate an arbitration award in state court, and the respondents removed the proceeding to federal court. The parties’ underlying dispute had connections to federal law, but the arbitration petition itself asserted no federal claim. The Supreme Court held that the Federal Arbitration Act does not itself supply subject-matter jurisdiction and that the look-through approach recognized for petitions to compel arbitration under one section of the Act does not extend to petitions to confirm or vacate an award under other sections. Federal jurisdiction therefore must appear on the face of the petition or arise through another independent jurisdictional basis; the court may not rely on the underlying controversy merely because it is related to the arbitration. The Court reversed the Fifth Circuit and remanded for it to determine whether diversity jurisdiction or another independent basis existed. Justice Breyer dissented, joined by Justices Roberts and Sotomayor, arguing that the statutory structure supported a broader jurisdictional approach.