Between 1959 and 1976, Cuba was a Communist state, led by Fidel Castro (1959-1964), then by Ernesto "Che" Guevara (1965-1976). The Cuban-American Conflict, a semi-open war between the country and the US between 1963 and 1969, was a noted event of the Cold War.
Castro took over in January, 1959, after a successful revolt against the dictatorship of Fulgencio Batista. In the first few years, no offence was made by either the US or Cuba, but the missile crisis in late-1962 evoked an open conflict between the two states. Cuba, backed up by the Soviet Union, made a constant threat to the national security of the United States. The conflict endured after Castro was assassinated in 1964, and, after a power struggle, Guevara took over and ordered an even more intensive fight against the US.