Justin Solomon | CNBC

On Sunday, the 704-passenger Adonia cruise ship is expected to sail from Miami, Florida, to Havana, Cuba. In doing so, the vessel is sailing into history — becoming the first U.S. leisure ship to voyage between the United States and Cuba in more than 50 years. The ship pulled out of the Port of Miami around 4pm ET, accompanied by a large contingent of police in the water and the Coast Guard in the air. The Adonia is part of Carnival's Fathom brand, based around so called "impact travel" where passengers not only take part in the usual cruise activities like eating, drinking and sun-bathing, but have the opportunity to learn from and work with locals in each port of call.

Passengers "will have free time and be able to go on your own a bit, so I'm not sure it will feel that different" from a full fledged leisure cruise, Carnival CEO Arnold Donald told CNBC in an on-board interview. He said the cruise was completely sold out, and there were about a dozen Cuban-born passengers on board. Those factors are what makes this legal. American's still cannot legally visit Cuba as tourists, but they can if they qualify for one of 12 categories, including "people-to-people" and "cultural exchange" programs offered under Fathom's umbrella. As protesters rode along the side of the ship, passengers lined the upper decks waving American and Cuban flags. Donald and Fathom president Tara Russell gave a short speech to the passengers, thanking the crew and employees that made the cruise happen. "We're delighted to be here," said Donald. "We're humbled, it's an honor, it's a privilege."

Other Carnival brands will be travelling to Cuba over time as port space becomes available, he said.

"This is not about going there like you would to another Caribbean Island and just going to hang out at the beach. This is not the purpose of this cruise," said travel expert Stewart Chiron, also known as "The Cruise Guy."

Still, the planned activities hardly seem to qualify as hard labor. Passengers will spend their days on shore excursions, where they will have options to experience dance and musical performances, meet with business owners, students and artists — all as part of their cultural exchange programs. The experience does not come cheap, however: A balcony room for two adults runs for nearly $9,000. "It's not cheap but we are still a better value if you were to go by air and book your own travel," Donald told CNBC. The Adonia will travel to Cuba every other week with stops in three ports of call; Havana, Cienfuegos and Santiago de Cuba. During the off weeks, the ship will be in the Dominican Republic on a similar impact travel trip. That trip however, comes at nearly a third of the cost. Chiron explained that the cost is "disproportionate compared to the same cruise on the same ship that is going to the Dominican Republic." However he added it's worth the money, especially considering the historical value. "Right now they are the only game in town so why leave money on the table? It is going to provide a very unique experience that no one else can offer," Chiron said.

The trip that almost wasn't

The trip almost didn't happen. Just weeks before the Adonia was set to leave Miami for Havana, Carnival came under heavy pressure from anti-Castro activists. At the time, the company said it would hold off on the trip until the Cuban government allowed Cuban-born Americans to travel to the island nation by sea — a prohibition against that had been on the books in Cuba for decades. Yet with just days to spare, the countries government made a concession — allowing Cuban born Americans to travel to Cuba by sea, something they had been allowed to do by air for years. With law changed, one can expect more cruise companies aiming their ships towards Cuba. Norwegian Cruise Line Holdings is one of those companies: The company's president and (Cuban-born) CEO Frank Del Rio said in a recent statement that Norwegian's Oceania brand "continues discussions with Cuban officials seeking approval to commence cruises to Cuba later this year." Del Rio added that he has "every confidence that the Cuban government would allow its natural born citizens to visit the island nation by cruise ship as they have allowed Cuban Americans to travel by air for years. I am very much looking forward to sailing to Cuba soon aboard one of our ships in the company of many fellow Cuban Americans and other fellow Americans who wish to share in the excitement and passion that cruising to Cuba brings." That said, there are lingering questions as to whether or not Cuba itself can handle the influx of tourists and cruise ships. Docking space is extremely limited throughout the island. That means companies which hope to send larger cruise vessels to the Island may have to consider using tenders to get passengers to and from the actual port. "There will have to be a lot of tenders to be able to transport passengers because they don't have the docking facilities to handle these large ships," Chiron said. "Countries have spent hundreds of millions of dollars building up their port infrastructure so this type of a boom is not going to happen overnight."