Bay of Pigs
Who: Fidel Castro helped to lead the Cuban Revolution in overthrowing the existing government of Cuba in 1959. He was an ardent communist and allied with Soviet Union.
What: The CIA was tasked with overthrowing Fidel Castro's government in Cuba. Lots of people from Cuba were called exiles. The CIA trained these exiles in guerrilla warfare. The idea was to sneak back into Cuba and begin a guerrilla war against Fidel Castro. The plan changed and it was to help the exiles of off the island.
Where: Cuba and the Bay of Pigs.
When: The invasion was on April 17th, 1961. It was planned long before then, though.
Why: The CIA was asked to overthrow Fidel Castro's government in Cuba.
Summary: In 1961 the United States sent trained Cuban exiles to Cuba to overthrow Fidel Castro's government. They failed miserably.