Marbury v. Madison
Marbury v. Madison (1803) was the first U.S. Supreme Court decision declaring constitutional limits to its own court powers.
Outgoing President John Adams had issued William Marbury a commission as justice of the peace, but the new Secretary of State, James Madison, refused to deliver it. Marbury then sued to obtain it. The Supreme Court decided, in Marbury v. Madison, that it did not have the constitutional power to give Marbury the commission because it found The Judiciary Act of 1789 to be "repugnant to the constitution" and thus "void", adding "that courts, as well as other departments, are bound by that instrument." Chief Justice John Marshall thereby refused to comply with The Judiciary Act, a result that pleased President Thomas Jefferson but using reasoning (declaring the Act to be "void") that was unacceptable to him. In finding the Court unauthorized to issue a writ of mandamus, Chief Justice Marshall stated that "if this court is not authorized to issue a writ of mandamus to such an officer, it must be because the law is unconstitutional."
The case was the first enactment of judicial review, and is often cited for stronger principles that the Supreme Court has the sole or final authority to interpret the Constitution. But the case only actually interpreted the Constitution to find limits on its own powers. It did not declare any act of Congress to be unconstitutional; it merely interpreted the Judiciary Act to be within constitutional bounds.
For example, within the text of the court's opinion, John Marshall wrote that:
The Constitution is either a superior, paramount law, unchangeable by ordinary means, or it is on a level with ordinary legislative acts, and, like other acts, is alterable when the legislature shall please to alter it. If the former part of the alternative be true, then a legislative act contrary to the Constitution is not law; if the latter part be true, then written Constitutions are absurd attempts on the part of the people to limit a power in its own nature illimitable.
The point that Marshall is making is that the Constitution, being superior to ordinary legislative acts, ordinary law, is changeable only by extraordinary means.
Progressives routinely cite Marbury as a foundational source for their claims of a Living and breathing constitution. In particular, their favorite line is "It is emphatically the province and duty of the Judicial Department to say what the law is." However, Marshall himself precluded such a notion by placing the Constitution above ordinary law.
Judicial Review vs Judicial Supremacy
Since the birth of Judicial Supremacy in 1958 in the court case Cooper v. Aaron, there has been some confusion as to how the Founding Fathers could have given such immense power to the court systems. In Cooper, the courts argued of Marbury that "This decision declared the basic principle that the federal judiciary is supreme in the exposition of the law of the Constitution." The problem is, Marbury does no such thing and neither did the Founders.
The words as Marshall wrote them in Marbury make a very plain argument for Constitutional Supremacy, not judicial supremacy. Many historians have noted that at the Constitutional Convention, in Federalist No. 78, as well as earlier court cases such as Hylton v. United States (1796), judicial review was being discussed or being employed prior to Marbury.
What this amounts to is a confusion of terms. Judicial review is a negative power, which in its strongest form merely strikes down laws and forces legislatures to come back another way, or not to come back at all.
Judicial supremacy is the belief that the courts have a positive power, which grants judicial agents the power to legislate from the bench.
In short, judicial supremacy and judicial review are not the same thing.