Cherimoyas are native to the Andean highlands but they grow in many areas of the world with warm days, cool nights, and dry, frost-free conditions. The appearance is a bit mysterious: "like a pre-columbian jade pinecone, or the finial for a giant Inca four-poster bed," as Elizabeth Schneider puts it.
The greenish leathery skin protects a custard like, cream-colored flesh tasting like a subtle blend of banana, pineapple, vanilla and papaya. Their peak season is from November to May.
The biggest obstacle is finding a cherimoya in good condition and letting it ripen properly. They bruise easily and have to be carefully packed and shipped by air. Once you have it home, let it ripen at room temperature until it yields to gentle pressure like a peach. Once ripe, Cherimoyas can be refrigerated for a few days.
For further Information, David recommends these readings:
Uncommon Fruits and Vegetables: A Commonsense Guide, by Elizabeth Schneider (Harper & Row, 1986)
1997 Cherimoya Handbook