Most Cuban exiles in the United States are both legally and self-described political refugees. This status allows them different treatment under US Immigration statutes than other Latin American immigrants. The exiles came in numerous discernible waves.
The first wave occurred after the Cuban revolution of 1959 led by Fidel Castro. A lot of the refugees came with the idea that the new government would not last long, and their stay in the US was temporary. Homes, cars, and other properties in Cuba were left with family, friends, and relatives, who would take care of them until the Castro regime would fall.
The second wave began in 1961 amid the nationalization of educational institutions, hospitals, private land, and industrial facilities. Additionally, the Castro government began a political crackdown on the opposition either incarcerating opponents or perceived opponents or executing the same. At this point, after the Bay of Pigs Invasion, Castro had gone from a self-proclaimed non-communist freedom fighter to a self-proclaimed Marxist-Leninist.
There was a smaller wave of refugees in 1965 from the Cuban port of Camarioca. Cuban exiles from Miami brought friends and relatives to Key West by using small leisure boats.
From 1965 through 1972, "Freedom Flights" from Havana to Miami transported thousands of Cuban refugees. Flights were limited to immediate relatives, with a waiting period anywhere from one to two years.
In 1980, probably one of the most impacting wave of exiles occurred during what became known as the Mariel Boatlift. The mass boatlift occurred after a number of Cubans drove a bus through the gates of the Havana Peruvian Embassy and requested asylum. One embassy guard died as a result of friendly fire when another guard machine gunned the incoming bus and hit the first one accidentally. When the Peruvian ambassador refused to return the exiled citizen to the authorities, Castro removed the Cuban guards from the embassy, basically opening the door to the 4,000 plus asylum seekers that came into the embassy within the next few days. Reacting to this unexpected and sudden exodus and embarrassed in front of the world media, Castro basically stated that "anyone who wants to leave Cuba can do so". This resulted in an even worse exodus through the port of Mariel, where an improvised flotilla of Cuban exiles from Miami in small pleasure boats and commercial shrimping vessels brought Cuban citizens who wished to leave the island. Within weeks, more than 125,000 Cubans reached the United States despite Coast Guard attempts to stem the movement. As the exodus became international news and an embarrassment for the Cuban government, Castro rounded up residents confined to insane asylums, hard-core criminals--not political--from prisons, and other "socially undesirables", forcing the incoming rescuers from Miami to take the worse elements from the island to the US if they wanted to leave Cuba with their friends and relatives. The scale of the exodus created political difficulties for both governments, and an agreement was reached to end the boatlift after several months. Out of more than 120,000 refugees, a significant number were believed to possess criminal records in Cuba, though published percentages on this vary widely--this can also be seen as part of the disclaimer at the end of "Scarface", where Al Pacino plays a criminal "marielito". After two years, most of the hardcore criminals had disappeared, either in federal prisons or dead, and the remaining population was quickly assimilated with the rest of the population.
During the past 10 years exile waves have consisted of "balseros" (rafters), who brave the rough seas in homemade rafts.