As of 2017, there are many airlines that operate direct flights to Cuba from the US.

Cuba Travel Services is a great resource for learning more about travel to Cuba. You can book a flight through their site as well as purchase the required travel visa.

Or to book your flight directly, here's the list of a few airlines that operate direct flights to Havana from from Los Angeles, Florida, and New York airports:

• Alaska Airlines - Flights departing from: LAX
• JetBlue - Flights departing from: JFK, Orlando, & Ft. Lauderdale
• SouthWest - Flights departing from: Tampa & Ft. Lauderdale
• Delta Airlines - Flights departing from: NYC, MIA, ATL
• United Airlines - Flights departing from Newark