The first wave arrived as near-destitute refugees, but over the decades the exiles have risen to become a potent force in American political life. Even as their wealth expanded and their children grew up as Americans, they stayed focused on one goal: toppling the communist dictator who drove them from their homes.
Such is the exiles' clout in the key swing state of Florida that American presidents of both parties have stuck to a 1960s policy of isolating Cuba economically with a trade embargo and refusing to deal with it diplomatically.
Even as the US normalised diplomatic relations with China, a far more powerful rival, and Vietnam, a country where half a million Americans died fighting communism, its policy towards Cuba remained frozen in time.
That consensus came crashing down when President Barack Obama announced that he was reopening the US Embassy in Havana and bringing Cuba in from the cold. "Today, America chooses to cut loose the shackles of the past so as to reach for a better future," he said.
The sense of anger and betrayal felt by older Cuban exiles is written across Miriam de la Pena's face. Her firstborn son, Mario, was a volunteer pilot with Brothers to the Rescue, a Miami activist group that flew sorties over the 145km of sea separating Florida from Cuba, looking for the makeshift rafts of Cubans trying to flee to the US.
On February 24, 1996, Cuban military jets shot down two of the Brothers' Cessna aircraft, killing Mario and three other pilots.
The FBI later concluded that the Brothers had been infiltrated by "the Cuban Five", a group of spies in Miami who helped the regime's air force to track and destroy Mario's aircraft.
One of the spies was convicted of conspiracy to murder and sentenced to life in an American federal prison - where he remained until Obama freed him last week as part of the diplomatic deal.
"The Obama Administration has trampled on the only little bit of justice we had," de la Pena said.
Obama's decision to risk the wrath of the Cuban exiles is partly a sign of an unbound second-term President, who will never face re-election and is on a streak of policy radicalism in his last two years in office.
In just the past six weeks, he has announced a major climate deal with China, an extension of nuclear negotiations with Iran and a promise to allow millions of illegal immigrants to stay in the US. But the White House has also calculated that the Cuban-American community is changing over time.
Cubans who arrived in the US more recently - and so actually lived part of their lives under the American trade embargo - are generally less supportive than those who fled in the 60s before the policies were imposed. A poll from Florida International University this year found, for the first time, a slight majority of Cubans in Miami supported an end to the embargo. That number leapt to 62 per cent among the young.
"There are differences in the generations," said Carlos Gimenez, the Cuban-American Mayor of Miami-Dade County.
"My views are a little different from my parents and my kids' are a little different from mine."
Like many others in Miami, Gimenez said he believed the embargo should be lifted, but that Obama had failed to extract any significant concessions from the Castro regime in return for easing US policy.
"I asked the White House is there anything in writing? There appears to be a lot of 'we wish, we hope, we expect' and nothing that's ironclad," Gimenez said.
Bryan Medina, a 19-year-old student, became an unwitting symbol of the generation gap when he went to an anti-Obama protest in Little Havana last week holding a sign showing the Cuban flag and the words "Goodbye embargo, Hello America".
Medina said the sign was meant to promote his band, Quantum Waves. But it provoked a furious reaction from older Cubans, some of whom tried to tear it from his hands.
"People were calling Obama an assassin and a communist," Medina said. "I think they're ignorant to say those things."
As the sun goes down over Little Havana, Oscar Rivera, 78, sits next to a memorial to those killed during the 1961 Bay of Pigs invasion, the disastrous Kennedy-era attempt to send exiles to overthrow the Castro regime.
Using the few words of English he had picked up in his 44 years in the US, he described his generation's frustration that president after president had not done more to end communism in Cuba.
"Kennedy: No good. Clinton: No good." As he reached the occupant of the Oval Office, his scowl deepened and he waved a rolled-up newspaper in his frustration. "Obama: No, no, no, no good."
4 aspects of Cuba debate
1. Political gambit
Democratic and Republican analysts alike see President Barack Obama's overtures to Cuba as an effort to break Republican claims on the Cuban-American vote, saying if tensions ease between the two countries, Florida's Cubans will be more likely to focus on other issues that Democrats use to appeal to Hispanics nationwide.
2. A future in Cuba?
Cuban law forbids foreigners from buying property on the island, but once diplomatic ties are re-established, some Cuban-Americans hope this will change. "This could completely change my future expectations about my relationship with Cuba", says Jovan Rodriguez, a young architect in Miami. "The truth is, I hope to be able to return soon."
3. A future in oil?
The thaw raises the possibility of Cuba getting its share of offshore oil in the Gulf of Mexico. There's real potential just off the island's northwest coast and Cubans desperate for economic growth welcome the opportunity, but analysts say a Cuban oil boom is unlikely anytime soon because of low oil prices and better drilling opportunities elsewhere.
4. Split opinions
A recent poll shows Cuban-Americans almost evenly split on re-establishing US ties to Cuba: 48 per cent disagree with Obama and 44 per cent agree. US-born Cubans strongly support Obama's plan, while those born on the island strongly oppose it. Cuban-Americans under 65 widely support it, while those over 65 strongly oppose it.
- AP
