A wealth of plant species used by humans for different purposes, but mainly as food, originated and domesticated in the Mesoamerican region. Papaya (Carica papaya) is the third most cultivated tropical crop worldwide, and it has been hypothesized that Mesoamerica is the most likely center of its origin and domestication. In support of it, many wild populations of papaya occur throughout Mesoamerica and hence represent the gene pool of genetic variability for further evolution and future crop management. Despite its importance, a dearth of information exists regarding the status of wild populations of papaya, as compared to the extent of knowledge, and interest, on domesticated varieties. We review the evidence on the extant wild populations of papaya, as well as its origin and distribution. Also, we synthetize what is known on the domestication history of the species, including the domestication syndrome that distinguishes wild and domesticated papayas. Moreover, we make an account of the use of genetic markers to assess genetic diversity of wild and domesticated papaya, and discuss the importance of papaya as the first species with a transgenic cultivar to be released for human consumption, and one that has its complete genome sequenced. Evidence from different disciplines strongly suggest that papaya originated and was domesticated in Mesoamerica, and that wild populations in the region possess, still, high genetic diversity compared to the domesticated papaya. Finally, we outline papaya as an excellent model species for genomic studies that will help gain insight into the domestication process and improvement of papaya and other tropical crops.