The Annonaceae family is one of the oldest angiosperms. The genus Annona is the one with the most species and, together with Asimina, the only ones that contain edible fruits. In the last 10 years, interest in these fruit species has increased, mainly due to their nutritional properties and their application in the treatment of human diseases. Mexico is the center of origin for most of them. However, at present much of the basic agronomic information, postharvest handling of the fruits, and their potential as new crops for areas with poor soils in organic matter or semi-dry climates is unknown. It is considered that these custard apple species may be an option to change towards instead of crops that have lost profitability and sustainability. A review of the current state of knowledge in different areas of the species A. muricata, A. macroprophyllata, A. reticulata, A. squamosa, and A. cherimola was carried out and to focus research efforts on the topics of greatest interest and on those where is required to achieve a sustainable production and use of these resources in Mexico. However, knowledge about the cultivation and potential uses of these species is needed to increase their commercialization; the integration of interdisciplinary and interinstitutional groups is required.
Keywords: Annona species; Annonaceae; bioactive compounds; biological activity; nutritional quality; perspectives; postharvest technologies.