Tensions ran highest during the first decades of the Cold War, from the mid-1940s through the mid-1970s, when the U.S. and U.S.S.R. engaged in a series of proxy wars such as the Korean conflict of the 1950s and Vietnam in the 1960s and 70s as well as the Cuban Missile Crisis of 1962.
Soldiers of the Soviet Union and the United States did not do battle directly during the Cold War. But the two superpowers continually antagonized each other through political maneuvering, military coalitions, espionage, propaganda, arms buildups, economic aid, and proxy wars between other nations.
