Fidel Castro was the man who overthrew the previous leader of Cuba and took his place
The Americans didn't like losing control over their own backyard as trading declined and business became nationalized
Castro established a close relationship with the USSR by trading sugar and oil for missiles
Castro became a communist himself in 1961
The bay of pigs happened when Kennedy got faulty military intelligence that if they invaded Cuba the Cubans would support them
He sent 1,500 troops only to discover that the Cubans quite liked Castro. The failure of the invasion was very embarrassing for the new president
Castro was not amused by this and turned to the soviets for help. The USSR sent over equipment to build nuclear missile bases in Cuba
US U2 spy planes captured a picture of missiles in Cuba and that was enough for Kennedy. It also showed soviet ships were on their way with further supplies