Judicial Review is the power to declare a law unconstitutional. This power is wielded by the Supreme Court. It makes the judicial branch a very powerful branch of the American government, because it involves overturning a legislative decision of Congress, and there is no way to override a Supreme Court decision except through a Constitutional Amendment.
Judicial review is never specifically mentioned in the Constitution, but instead is perhaps implied in Article III:
"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."
Judicial review is, however, mentioned by Alexander Hamilton in The Federalist Papers, and was established in the landmark case Marbury v. Madison in 1803 by the ruling of Chief Justice John Marshall. It is now a well established power of the Supreme Court, despite its how debatable its Constitutionality may be.[1][2] [3]