"The Judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish.... The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority...."
-- Article III, Sections 1 & 2,
The Constitution of the United States
The Supreme Court is the most visible of all the federal courts. The number of Justices is determined by Congress rather than the Constitution, and since 1869, the Court has been composed of one Chief Justice and eight Associate Justices. Justices are nominated by the President and confirmed by the Senate.
The Supreme Court considers very few cases each year. Most of these are the result of the Court's granting a writ of certiorari -- a petition to the Court to have a case heard. If four of the nine Justices consider a case to be worthy of review, a writ is granted.
Some cases are heard because they fall within the Court's "original jurisdiction." These include cases between the federal government and a state; two or more states, or a state and citizen of a different state; or cases involving diplomats or other foreign ambassadors.
Cases brought to the Supreme Court generally address important federal matters, such as when a right guaranteed by the Constitution is denied by a state, or when a state law is found to be in conflict with federal law.