Many countries have had controversial and difficult pasts, but Cuba's is exceptionally eventful. Since its discovery, it has been colonized, run by outsiders, invaded, and seen the rise of communism in the form of Fidel Castro. To understand the current relationship between the U.S. and Cuba one must understand the history between the two countries. From Spain to the U.S. Cuba has had to struggle for independence.
Cuba was originally a Spanish colony. Then in 1823, Thomas Jefferson talked of annexing Cuba, but never acted upon it. Cuba gained their independence from Spain in December of 1898 . After the Spanish American War of 1898, the U.S. had extended rule to both Cuba and Puerto Rico. Under the Platt Amendment of 1901, the U.S. had many powers within the Cuban Constitution. The U.S. had the ability to intervene in Cuban affairs and to set up a naval base in Cuba. That base in Guantanomo Bay still exists to this day. Also, the amendment limited Cuba's ability to run foreign policy. Although the U.S. held all of this power, Cuba was technically independent from the U.S. in 1902.
After 1950, things in Cuba began to escalate. Batista ruled as a dictator from 1952 until 1959. Under Batista, Cuba was a regular vacation spot for American families. But, the mob had many strongholds in Cuba. In fact, many mob families had large hubs in Cuba. Within Cuba itself, there was much corruption and poverty. Batista's brutal dictatorship allowed the rise of Fidel Castro.
On January 1, 1959 Fidel Castro came into power. As a revolutionary, Castro had few problems gaining control over the Cuban government. He promised a Cuba for the people and therefore was actually fairly well received by the general public. But, the U.S. wasn't ever in favor of Castro. Early on the U.S. tried to prevent what came to be called the Cuban Revolution.
One of those steps happened to be the Bay of Pigs. Few people can talk about the Bay of Pigs without cringing.