In 1959, Fidel Castro overthrew General Fulgencio Batista, the nation's US-backed president. At the time, American corporations owned almost half of Cuba's sugar plantations and a majority of its utilities. Without pro-American Fulgencio Batista, there would be less support for American corporations. Castro disliked their influence in Cuba, saying "Cuba sí, Yanquis no", which become one of his most popular slogans.
So, in 1960, President Dwight D. Eisenhower authorized the CIA to begin training 1400 Cuban exiles to overthrow Castro. The US couldn't directly attack Cuba, which was recently allied with the Soviet Union, or else they'd retaliate. So, if their secret plan went according to plan, it would spark an anti-Castro movement in Cuba, and it would eventually lead to overthrowing Castro.
The plan was to destroy Castro's small air force, so the military couldn't resist the invaders. However, Castro knew about the plan, and he moved his planes out of harm's way. The next step of the plan was to was to invade at an isolated spot in Southern Cuba, called Bay of Pigs. From the beginning, it was a failure, with a Cuban radio station reporting everything the US was doing, along with paratroopers landing in the wrong place, and US ships sinking after hitting coral reefs. In less than a day of fighting, 114 US were killed, and over 1,100 were taken prisoner.
Overall, the plan was a failure, and since then, no attempts of war/espionage have occurred besides Operation Mongoose, where they tried to kill Castro through the mafia.