Section 1 of Article III establishes the judicial branch of the federal government, vesting judicial power in 'one supreme Court' and in any inferior courts that Congress may choose to establish from time to time. This structure left the creation of the lower federal judiciary to legislative discretion, implemented immediately via the Judiciary Act of 1789. To safeguard judicial independence from political pressure, Section 1 guarantees that federal judges hold their offices 'during good Behavior' — effectively life tenure — and ensures their compensation cannot be diminished during their time in office.

Section 2 delineates the jurisdiction of the federal courts, defining the types of cases they are legally authorized to hear. Federal judicial power extends to all cases arising under the Constitution, federal laws, and treaties, as well as disputes involving ambassadors, maritime law, controversies where the United States is a party, and conflicts between different states or citizens of different states. It explicitly divides the Supreme Court's jurisdiction into original jurisdiction (cases heard directly, such as those involving ambassadors or states) and appellate jurisdiction (cases reviewed on appeal from lower courts), subject to regulations made by Congress. It also guarantees a jury trial for all federal crimes, except impeachment.

Section 3 provides a narrow, precise definition of treason, making it the only crime explicitly defined within the body of the Constitution. The Framers did this to prevent the federal government from using broad or politically motivated charges of treason to silence dissent, a tool frequently abused by European monarchs. Treason is defined strictly as levying war against the United States, or adhering to their enemies by giving them aid and comfort. Conviction requires the testimony of two witnesses to the same overt act, or a confession in open court. It further protects the families of those convicted by prohibiting the 'Corruption of Blood,' meaning punishment cannot extend to the descendants of the traitor.