Giant sheep or argalis (Ovis ammon Linnaeus, 1766) were classified into subspecies according to the nuptial coat of large males. Seven subspecies are recognized: nigrimontana, hodgsoni, jubata, darwini, ammon, polii, and karelini; kozlovi is a possible subspecies. The occurrence of dwarf argalis in Mongolia suggests that other subspecies may be described. This review corrects errors in earlier taxonomic studies based on inadequate understanding of seasonal and age-related pelages, invalid taxonomic criteria (morphometry without correction for allometry and the effects of muscular work), body size (without evidence for heritability), geographic location (not part of the specimen, and unverifiable), misunderstandings due to language barriers, and mislabelled or altered specimens and data. A key is included. New insights concerning argali biology emerged.