The United States and Cuba signed a deal Tuesday, February 17, 2016, restoring commercial air traffic. The flights will likely open up for people as early as this fall. Right now the only flights that operate between the countries are charter flights.
Note, for now, U.S. visitors to Cuba will still have to qualify under one of the travel categories legally authorized by the U.S. government. Tourism is not one of them. But the number of legal reasons to go to Cuba is long and it has become much easier to fit into a legal category. Commercial travel will give travelers the ability to simply check an online box on a long list of authorized categories.