Cuban authorities have closed down private movie theatres on their island (renegade screenings of the new Thor are a pressing socio-economic concern), proving once more that what the free market does on its own in the capitalist world, central planners must accomplish under communism.
But that’s politics. Art is art, and Cuba has a rich cinematic history. Wikipedia has a good overview and IMDb user TheWanderingFish has a viewing list to get you (me) started. YouTube is also a friend. For example, here’s Tomás Gutiérrez Alea’s classic Fresa y chocolate: