Most have headed for the US over the border with Mexico, along with many thousands from other countries.
Cuba saw its largest exodus of people last year since Fidel Castro’s revolution in the 1950s.
It has become a political crisis for the US and President Joe Biden has announced new measures.
More visas will be granted for some going through official channels, but those who just turn up at the border will face harsher action.
So what’s causing this mass exodus?
And can conditions change for the people of Cuba?
Presenter: Laura Kyle
Rosa Maria Paya – Founder of Cuba Decide, a movement to shift political and economic systems in Cuba.
Helen Yaffe – Senior lecturer in economic and social history at the University of Glasgow.
Andrew Selee – President of the Migration Policy Institute, Washington, DC.