Ommastrephidae was first established by the Danish zoologist Japetus Steenstrup in 1857.
It is classified under the suborder Oegopsina of the order Teuthida (squids).
It is divided into three subfamilies - Illicinae, Ommastrephinae, and Todarodinae; further subdivided into 11 genera and more than 20 species.

These subfamilies, genera, species, and subspecies are classified under Ommastrephidae:
Family Ommastrephidae
Subfamily Illicinae
Genus Illex
Illex argentinus, Argentine shortfin squid
Illex coindetii, southern shortfin squid
Illex illecebrosus, northern shortfin squid
Illex oxygonius, sharptail shortfin squid
Subfamily Ommastrephinae
Genus Dosidicus
Dosidicus gigas, Humboldt squid, jumbo flying squid or jumbo squid
Genus Eucleoteuthis
Eucleoteuthis luminosa, striped squid or luminous flying squid
Genus Hyaloteuthis
Hyaloteuthis pelagica, glassy flying squid
Genus Ommastrephes
Ommastrephes bartramii, neon flying squid or red flying squid
Genus Ornithoteuthis
Ornithoteuthis antillarum, Atlantic bird squid
Ornithoteuthis volatilis, shiny bird squid
Genus Sthenoteuthis
Sthenoteuthis oualaniensis, purpleback squid or purpleback flying squid
Sthenoteuthis pteropus, orangeback squid or orangeback flying squid
Subfamily Todarodinae
Genus Martialia
Martialia hyadesii, sevenstar flying squid
Genus Nototodarus
Nototodarus gouldi, Gould's flying squid
Nototodarus hawaiiensis, Hawaiian flying squid
Nototodarus sloanii, Wellington flying squid or New Zealand arrow squid
Genus Todarodes
Todarodes angolensis, Angola flying squid
Todarodes filippovae, Antarctic flying squid
Todarodes pacificus, Japanese flying squid or Japanese common squid
Todarodes pusillus, little flying squid
Todarodes sagittatus, European flying squid
Genus Todaropsis
Todaropsis eblanae, lesser flying squid
Ommastrephidae was first established by the Danish zoologist Japetus Steenstrup in 1857. It is classified under the suborder Oegopsina of the order Teuthida (squids). It is divided into three subfamilies - Illicinae, Ommastrephinae, and Todarodinae; further subdivided into 11 genera and more than 20 species.
These subfamilies, genera, species, and subspecies are classified under Ommastrephidae:
Family Ommastrephidae
Subfamily Illicinae
Genus Illex
Illex argentinus, Argentine shortfin squid
Illex coindetii, southern shortfin squid
Illex illecebrosus, northern shortfin squid
Illex oxygonius, sharptail shortfin squid
Subfamily Ommastrephinae
Genus Dosidicus
Dosidicus gigas, Humboldt squid, jumbo flying squid or jumbo squid
Genus Eucleoteuthis
Eucleoteuthis luminosa, striped squid or luminous flying squid
Genus Hyaloteuthis
Hyaloteuthis pelagica, glassy flying squid
Genus Ommastrephes
Ommastrephes bartramii, neon flying squid or red flying squid
Genus Ornithoteuthis
Ornithoteuthis antillarum, Atlantic bird squid
Ornithoteuthis volatilis, shiny bird squid
Genus Sthenoteuthis
Sthenoteuthis oualaniensis, purpleback squid or purpleback flying squid
Sthenoteuthis pteropus, orangeback squid or orangeback flying squid
Subfamily Todarodinae
Genus Martialia
Martialia hyadesii, sevenstar flying squid
Genus Nototodarus
Nototodarus gouldi, Gould's flying squid
Nototodarus hawaiiensis, Hawaiian flying squid
Nototodarus sloanii, Wellington flying squid or New Zealand arrow squid
Genus Todarodes
Todarodes angolensis, Angola flying squid
Todarodes filippovae, Antarctic flying squid
Todarodes pacificus, Japanese flying squid or Japanese common squid
Todarodes pusillus, little flying squid
Todarodes sagittatus, European flying squid
Genus Todaropsis
Todaropsis eblanae, lesser flying squid
Ommastrephidae