Discontent with our closest island neighbor began when Fidel Castro fell into power in January 1959 as a communist dictator of Cuba.

The U.S. wasn’t happy with Castro because he was a communist and he did not support American military presence on the island.  Castro did not approve of the United States interfering with Cuba’s natural resources or politics, so the U.S.took that as a threat. Castro even went as far as to “establish diplomatic relations” with the Soviet Union. In response to the soviet relation with Nikita Kruschev, the United States boycotted the importation of Cuban sugar.

Many Cubans fled to the United States when Castro came to power because he restricted basic civil and political rights and imprisoned anyone who was seen as a threat to his power.

Kennedy’s original plan for the Bay of Pigs was to invade Cuba as a surprise attack to hopefully start an anti-Castro uprisings among the natives. He also knew that the Soviets would get involved if word of the attack got out, so it really had to be kept quiet. I don’t know how you can sail into enemy territory and keep it a secret.

As you could imagine, word of the attack did get out and Castro withdrew his air force to avoid being a target. So, step one failed. Even the geography defeated this unsupported secret CIA project of sending Cuban Americans as an invading force before it had a chance.

Coral reefs sank U.S. ships! Backup paratroopers landed in the wrong place! It was an absolute disaster on the United States’ part and they surrendered after less than a day of fighting, and losing over 1,100 men as prisoners. 

The attack at the Bay of Pigs proved to be nothing but a sad, and embarrassing loss for the United States during the Cold War.  It came one year before the most tense crisis of the long 45 year struggle when US spy planes discovered soviet nuclear missiles in Cuba.  This time period in the fall of 1962 would later be known as the Cuban missile crisis.  It was the closest we have come to nuclear war and it was only resolved through power diplomacy known as brinksmanship.

http://www.history.com/topics/cold-war/bay-of-pigs-invasion

The photo below is from a 2014 public appearance of Fidel Castro. His brother Raul is now in power in Cuba and relations with the US are finally improving.