Living opossums (Didelphidae) comprise 125 species in 18 genera and 4 subfamilies. This synopsis lists all the didelphid taxa (subfamilies, tribes, genera, subgenera, and species) currently recognised as valid, summarizes information about typification, synonyms, and geographic distributions, remarks noteworthy recent changes in usage, and comments on still outstanding problems. A concluding discussion rejects the notion that the almost twofold increase in opossum species from 1993 to the present is “taxonomic inflation” and considers the impact of new kinds of data and new methods of data analysis on species delimitation.