The word "pstk" [pistag], used in the ancient Persian language, is the linguistic root from which the current name "pistachio", used worldwide, derives. The word pistachio is generally used to designate the plants and fruits of a single species: Pistacia vera L. Both the plant and its fruits have been used by mankind for thousands of years, specifically the consumption of its fruits by Neanderthals has been dated to about 300,000 years ago. Native to southern Central Asia (including northern Afghanistan and northeastern Iran), its domestication and cultivation occurred about 3000 years ago in this region, spreading to the rest of the Mediterranean basin during the Middle Ages and finally being exported to America and Australia at the end of the 19th century. The edible pistachio is an excellent source of unsaturated fatty acids, carbohydrates, proteins, dietary fiber, vitamins, minerals and bioactive phenolic compounds that help promote human health through their antioxidant capacity and biological activities. The distribution and genetic diversity of wild and domesticated pistachios have been declining due to increasing population pressure and climatic changes, which have destroyed natural pistachio habitats, and the monoculture of selected cultivars. As a result, the current world pistachio industry relies mainly on a very small number of commercial cultivars and rootstocks. In this review we discuss and summarize the current status of: etymology, origin, domestication, taxonomy and phylogeny by molecular analysis (RAPID, RFLP, AFLP, SSR, ISSR, IRAP, eSSR), main characteristics and world production, germplasm biodiversity, main cultivars and rootstocks, current conservation strategies of both conventional propagation (seeds, cutting, and grafting), and non-conventional propagation methods (cryopreservation, slow growth storage, synthetic seed techniques and micropropagation) and the application of computational tools (Design of Experiments (DoE) and Machine Learning: Artificial Neural Networks, Fuzzy logic and Genetic Algorithms) to design efficient micropropagation protocols for the genus Pistacia.