Much of the higher classification of Recent cephalopods is unstable. Various authors have suggested highly varying arrangements. We adopt a conservative arrangement that does not differ much from that of Naef (1921-23). Except for the position of the Octopodiformes and its two orders, we have a questionable phylogenetic basis for accepting this or any other scheme. We suggest, however, for the sake of stability, that the following classification be used until this or an alternative arrangement can be derived from cladistic analyses. The analyses, whether molecular or morphological, however, must be robust and must survive considerable scrutiny before changes in classification should be adopted. Nevertheless, we have adopted recent changes in the incirrates octopods (Strugnell et al., 2013) based on extensive data involving both morphology and molecular approaches with emphasis on the latter.