As a result of Cuba's communist tag, the U.S. severed all relations with Cuba. Cuba, in search of a market for its goods, quickly aligned itself with a fellow communist nation, the USSR. This further infuriated the U.S. government. In April of 1961, the U.S. and anti-Castro Americans attempted to covertly invaded Cuba. The attack failed miserably; The Cuban army was anxiously waiting for the invaders.
In June of 1961, President Kennedy declared a full trade embargo on Cuba and had the island expelled from the Organization of American States.
The Russian-Cuban relationship increased to the point where Russian President Khrushchev decided to install missiles capable of hitting Miami, in Cuba. They would serve as a bargaining agreement with the U.S.
The Soviet Union collapsed in 1991, leaving Cuba to fend for itself. The economy has been slow to recover to this day. Meanwhile, U.S.-Cuban relations remain strained.