Hi there!
1. The Bay of Pigs invasion (1961): an invasion supported by the CIA. The goal was to overthrow the communist government of Fidel Castro.
2. The Cuban Missile Crise (1962): a consequence of the first incident. Due to the US invasion, Cuba decided to cooperate with the Sovjet-Union and due to this relationship, the SU was planning to build a missile base on Cuba. This was the base of an (unarmed) conflict.