In 1976, Cuba joined COMECON. That was the economic program of the Soviet bloc, whose sugar Cuba was now to supply.
Cuba began helping to export Revolution. Although Khrushchev once said, "Revolutions are not made for export," the Soviet Union followed and assisted.
President Jimmy Carter announced that the United States was willing to accept Cuban refugees with "open arms." In response, Castro let 120,000 people leave the island for the US. Many left voluntarily, others were unwanted dissidents and violent criminals. The US had to accept them, causing Carter a great deal of embarassment. The entire fiasco became known as the Mariel Boatlift, named after the port city through which many of the refugees left.
In 1983, one day after hundreds of marines were killed in the Middle East, Reagon invaded Granada. The Cuban-backed Government there was overthrown only after Cubans died fighting the invaders.
In the late 1980s, Soviet aid lessened. Eventually, many Soviet bloc Governments were destroyed. This cost Cuba the majority of its trade.
President Castro announced that a Special Period would occur. Economic conditions became much worse, and many Cubans left the island.
In 1992, the Torricelli Act was passed. This law basically made the American blockade equivalent to the Soviet blockade of West Berlin. The law hadn't done that before for the purpose of being consistent with Capitalist propaganda. Now that no one noticed, the US could afford to appear hypocritical.
On February 24, 1996, the Cuban air force shot down two planes flown by anti-Castro exiles who had violated Cuba's national sovereignty.
The American press made such a big deal out of it, President Clinton was forced to sign the Helms-Burton Act to win Florida in the next election. This law has been a disaster for the United States. Its European allies have turned against it and President Castro has become even more powerful in Cuba.