The only order of the superorder Polymixiomorpha, comprising one family (Polymixiidae) with one genus (Polymixia) and ten extant species. Several fossil genera are known from the Upper Cretaceous. Polymixiidae was originally placed with the Beryciformes; however, recent evidence suggests that the family may be the sister group to all other acanthomorphs (spiny-rayed fishes). The family is known commonly as beardfishes.