Commercial flights between the US and Cuba are going to return later this year and DOT just tentatively awarded the 20 daily frequencies to Havana (there are other cities awarded as well).
These will be scheduled flights where passengers are able to purchase tickets directly. Currently there are various charter flights that are arranged by travel agencies. These are not eligible for mileage accrual, although operated by airlines such as American.
You can access the DOT’s release here:
It is about the time for the US and Cuba have direct air link that passengers from the US and those transiting via the US can purchase tickets to. Currently, many US passengers transit to Cuba via Mexico or via Central America.
Many European airlines offer direct service to Havana including Air Berlin, Condor, KLM, Air France, Aeroflot, Virgin Atlantic plus number of charters.
It is interesting to see how much pending demand there is from the US for travel to Cuba. Americans no longer need to apply for the permission to travel but they still shouldn’t travel purely on a “tourist” trip. Also, the hotel infrastructure in Havana is dreadful. I have been there twice.