Cuba got involved in the Cold War when the United States broke off its diplomatic relations with Cuba in 1961, and Soviet Union increased their economic aid to Cuba.
In 1961, the USA planned the Bay of Pigs invasion of Cuba, intending to overthrow the head of Cuban state (Fidel Castro), who was backed by the Soviet Union. However, the operation failed.
Fidel Castro then appealed to the Soviet Union for military help, to which Soviet Union decided to set up nuclear missile launchers in Cuba (only 90 kilometers from Florida) aimed at the USA.
Cuban Missile Crisis (called October Crisis in Cuba and Caribbean Crisis in Russia) brought two superpowers on the brink of a nuclear war. However, the crisis was averted diplomatically.
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