Descriptions and diagnoses are alternative choices in all Codes of Nomenclature because Linnaeus relied on diagnoses, not descriptions, to name ca. 13,400 animals, plants, and fungi. A diagnosis names characters in which a new taxon differs from the most similar known taxon; a description mixes taxonomically informative and uninformative features, usually without indicating which is which. The first formal diagnoses of new taxa that included DNA-based characters came out in 2001, and by November 2015, at least 98 names of species of acoels, lichens, angiosperms, annelids, alveolates, arachnids, centipedes, turtles, fishes, butterflies, mollusks, nematodes, and pathogenic fungi have been published based on diagnostic mitochondrial, plastid, or nuclear DNA substitutions, indels, or rarely genetic distances, with or without additional morphological features. Authors have found diverse ways to specify the diagnostic traits (all published studies are here tabulated). While descriptions try to "cover" within-species variation, a goal rarely accomplished because of (i) the stochastic nature of specimen availability (thousands of species are known from single collections) and (ii) the subjective circumscription of species, the purpose of diagnoses was and is speedy identification. Linnaeus tried to achieve this by citing images, geographic occurrence, and previous literature. The renewed attention to sharp diagnosis now coincides with worldwide barcoding efforts, may speed up formal naming, and matches the increasing reliance on DNA for both classification and identification. I argue for DNA-based diagnoses of new species becoming a recommendation in all Codes, not just the bacterial code. [Codes of Nomenclature; description; diagnosis; DNA-based diagnosis; naming new species; nomenclature.