Right now loads of large, heavy, coarse-coated, ovoid zapote mameys are piled on pickups and wheelbarrows, some cut open and shaped as flowers or stars to show their deep salmony flesh, on the streets of Coatepec. They are grown in enough abundance to provide such heaps, but I don't think they have yet become a commercial crop of the industrial agriculture sort: I don't think there are giant orchards of them anywhere. They are, in fact, referred to in a UN publication as a "neglected crop." But they are being considered for use in restoration of local agriculture for providing for local people. AND some consideration to the development of an export market is being given. The questions people ask for this possibility include the use of preservatives on the skins, effects of refrigeration and so forth. AND there is a need to know whether there would be or could be a market abroad for such fruit. Just ask me! There already is a small market abroad for frozen mamey.
I love zapote mameys, scientifically known as pouteria sapata. They are indigenous to the lower altitudes of Veracruz as well as humid, warmer areas in a number of other Mexican states and some of Central America. Here is a picture I took to show you a whole one, some slices, and the seed. The seed, except for a natural split area in the outer coating, is quite shiny, like polished dark wood.

Sometimes I just cut one open and scoop out and eat the flesh. It has a kind of sweet-potatoey-peachy flavor with an avocado texture. Sometimes I cut hunks to put on cereal. One will last me four days.
Here is a good basic article on mamey zapotes from Wikipedia. A more detailed article can be found here. You'll recognize this as the source for a fair amount of what I say about them.
You don't see them so much anymore, but there used to be tons of street vendors that sold pieces of fruit wrapped in paper with various kinds of chili powder sprinkled on top. We always avoided these because of fear of germs. On our part, this was definitely reasonable, but most Mexicans I know ate the stuff freely. I think a good investment would be to develop some easy to use knife and fruit cleaning solution and to maybe encourage use of hand sanitizers and have a renaissance of these stands....so much better than junk food, to buy a shell of diced zapote sprinkled with chiles! And they are loaded with nutritious stuff.
Otherwise, you can pretty well use them for the same things you use other fruits for: syrups, smoothies, ice cream and so on. The seeds, ground up, can be used in making chocolate and in making soaps and shampoos and other skin products as well as for a number of pharmaceutical products as can the leaves and unripe fruit. The sap can be used in chewing gum. The wood is strong and useful as lumber.
The hope is that mamey zapote trees, which can also shade coffee plantations will increase in importance in the development of sustainable forestry/agroforestry projects. Not only is the tree and its fruit useful as product, but the tree itself contributes to soil improvement and mitigates erosion and apparently is beneficial in keeping away insect pests from other crops planted with it.
Mamey and other fruits from the Caribbean-Mesoamerican area are finding homes in South Florida. Here is a clip of a talk on Mamey trees from Fruitscapes, a University of Florida extension website. It has lots of information about mangoes, avocadoes, and other fruits, too.
While I was zipping around looking for online information on mamey zapote, I came across this delightful cooking site in Spanish. Check it out!