On December 3rd 1989 the Cold War was declared officially over - although the precise dates are actually argued, with 1991 being put forward as the end date, when the Soviet Union itself dissolved.
After World War II both the United States and the Union of Soviet Socialist Republics became the two dominant powers - the superpowers - of the world. The end of World War II saw many former Nazi-occupied countries and allies annexed by the Soviet Union. Philosophical differences, and both powers having the atom bomb, resulted in a war through proxies that lasted for decades.
The Malta Summit between US President George H.W. Bush an U.S.S.R. President Mikhail Gorbachev, several weeks after the fall of the Berlin Wall, resulted in the leaders declaring the Cold War to be over.
Image: By David Valdez (1949-) [Public domain], via Wikimedia Commons (commons.wikimedia.org/wiki/File:Bush_and_Gorbachev_at_the_Malta_summit_in_1989.gif)