The landmark Supreme Court decision that established judicial review in the United States is Marbury v. Madison, decided in 1803. This case established the principle that the Supreme Court has the authority to review acts of Congress and determine their constitutionality. The decision asserted the judiciary's role as a co-equal branch of government, enabling it to check the powers of the executive and legislative branches. This ruling was a crucial step in defining the balance of power within the U.S. government and laid the groundwork for the exercise of judicial review in subsequent cases, solidifying the judiciary's influence in American law.