After Qiao, King, Long, Ahlberg & Zhu, 2016

<==o Gnathostomata Gegenbaur, 1874 (jawed vertebrates; leualliset selkärankaiset)
   `==o †Placodermi McCoy, 1848 [Placodermiomorphi] (placoderms; panssarikalat)
      |-- †Brindabellaspis stensioi Young, 1980 [Brindabellaspida Gardiner, 1993]
      |-- †Antiarchi Cope, 1885
      `--+-- †Romundina stellina Orvig, 1975 [Palaeacanthaspidae]
         `--+-- †Petalichthyida Jaeckel, 1911 [Petalichthyiformes]
            `--+-- †Arthrodira Woodward, 1891
               `--+-- †Asterosteidae [Rhenanida Broili, 1930]
                  `--+-- †Entelognathus primordalis Zhu, Yu, Ahlberg, Choo, Lu, Qiao, Qu, Zhao, Jia, Blom & Zhu, 2013; L.Sil. EAs.
                     `--o Eugnathostomata [paraphyletic Acanthodii Owen, 1846]
                        |-- †Janusiscus schultzei Giles, Friedman, & Brazeau, 2015
                        |-- †Ramirosuarezia boliviana Pradel, Maisey, Tafforeau & Janvier, 2009
                        |--o Osteichthyes Huxley, 1880 [Neoteleostomi] (bonefishes; luukalat)
                        |  |?- †Naxilepis gracilis Wang & Dong, 1989
                        |  |--o †Dialipina Schultze, 1968
                        |  |  |-- †D. salgueiroensis Schultze 1968
                        |  |  `-- †D. markae Schultze, 1992
                        |  `--+--o †Ligulalepis Schultze, 1968 [alternative position 1]
                        |     |  |?- †L. yunnanensis Wang & Dong, 1989 [scales]
                        |     |  `-- †L. toombsi Schultze, 1968
                        |     |-- Sarcopterygii Romer, 1955 (flesh-finned bonefishes, including tetrapods; lihaseväiset luukalat)
                        |     `-- Actinopterygii Klein, 1885 (non? Cope, 1887) (viuhkaeväiset luukalat; ray-finned bonefishes)
                        |--o †Culmacanthidae [paraphyletic Diplacanthiformes Berg, 1940]
                        |  `--o †Culmacanthus Long, 1983
                        |     |-- †C. pambulensis Young, 1989b
                        |     `-- †C. stewarti
                        |--o †Tetanopsyridae [paraphyletic Diplacanthiformes Berg, 1940]
                        |  `--o †Tetanopsyrus Gagnier et al., 1999; L. Dev. NNA.
                        |     |-- †T. lindoei Gagnier et al., 1999
                        |     `-- †T. breviacanthis Hanke, Davis & Wilson, 2001
                        |--o †Lophosteus Pander, 1856 [Lophosteiformes Gross, 1969: †Lophosteidae Gross, 1969]
                        |  |-- †L. superbus Pander, 1856
                        |  |-- †L. connexus Märss, 1986
                        |  `-- †L. ohesaarensis Schultze & Märss, 2004
                        |--o †Diplacanthidae Woodward, 1891 [paraphyletic Diplacanthiformes Berg, 1940]
                        |  |-- †Gladiobranchus Bernacsek & Dineley, 1977; L. Dev. NNA.
                        |  |-- †Diplacanthus Agassiz, 1844 [Rhadinacanthus] M. Dev. Eu. EEu. U. Dev. NA.
                        |  |?- †Ptychodictyon Gross, 1973; L.Dev. WNAm., M.Dev. EEu.
                        |  `-- †Rhadinacanthus Traquair, 1888
                        `--+--+-- †Ischnacanthiformes Berg, 1940
                           |  `-- †Acanthodiformes Berg, 1940 [Acanthodidae Huxley, 1861 sensu Carroll, 1988]
                           `==o Climatiiformes Berg, 1940
                              |-- †Latviacanthus ventspilsensis Schultze & Zidek, 1982; L. Dev. EEu.
                              `--+-- †Brochoadmones milesi Bernacsek & Dineley, 1977; E.Dev. WNAm. [Brochoadmoidei Gagnier & Wilson, 1996a: †Brochoadmonidae Bernacsek & Dineley, 1977]
                                 |--o †Kathemacanthidae Gagnier & Wilson 1996
                                 |  |?- †Knerialepis mashkovae (Karatajùtë-Talimaa, 1997) Hanke & Karatajute-Talimaa, 2002 [Kneria mashkovae Karatajùtë-Talimaa, 1997; non Kneria Steindachner, 1866]
                                 |  |?- †Seretolepis elegans Karatajute-Talimaa, 1968
                                 |  `-- †Kathemacanthus rosulentus Gagnier & Wilson 1996; E.Dev. WNAm.
                                 |--o †Vernicomacanthus Miles, 1973, L. Dev. Eu. [paraphyletic Climatiidae]
                                 |  |-- †V. uncinatus
                                 |  `-- †V. waynensis
                                 |--o †Climatiidae Berg, 1940 sensu stricto??
                                 |  |-- †Ptomacanthus Miles, 1973, L. Dev. Eu. EEu.
                                 |  `--+-- †Climatius Agassiz, 1845, U. Sil. L. Dev. Eu. NA. EEu.
                                 |     `--+-- †Brachyacanthus Egerton, 1860, L. Dev. Eu. 
                                 |        `-- †Parexus Agassiz, 1845, L. Dev. Eu.
                                 `--+--+-- †Lupopsyrus pygmaeus Bernacsek & Dineley, 1977, E.Dev. WNNAm.
                                    |  `-- †Obtusacanthus corroconis Hanke & Wilson 2004
                                    `--+-- †Gyracanthides Woodward, 1906; Miss. Aus. [Gyracanthidae Woodward, 1906]
                                       `-- Chondrichthyes Huxley, 1880 [Chondrichthiomorphi] (rustokalat; sharks & rays)

Basal gnathostomes not included in Qiao et al. 2016

    “Placodermi” McCoy, 1848
        †Stensiolla heintzi [Stensioellida Carroll, 1988: Stensioellidae]Paraplesiobatidae Berg 1940 [Pseudopetalichthyida Denison 1975; Pseudopetalichthyiformes]Nessariostoma granulosum Broili, 1933
            †Paraplesiobatis heinrichsi Broili, 1933
            †Pseudopetalichthys problematica Moy-Thomas, 1939 [Parapetalichthys Kuhn, 1949]
        †Phyllolepididae Agassiz, 1844 [Phyllolepida Stensiö, 1934]Ptyctodontidae Gross, 1932 [Ptyctodontida Gross, 1932]



After Brazeau, 2009, and Davis, Finarelli & Coates, 2012

<==o Gnathostomata Gegenbaur, 1874 (jawed vertebrates; leualliset selkärankaiset)
   `==o †Placodermi McCoy, 1848 [Placodermiomorphi] (placoderms; panssarikalat)
      |?- †Brindabellaspis stensioi Young, 1980 [Brindabellaspida Gardiner, 1993]
      |?- †Stensiolla heintzi [Stensioellida Carroll, 1988: Stensioellidae]
      |?-o †Paraplesiobatidae Berg 1940 [Pseudopetalichthyida Denison 1975; Pseudopetalichthyiformes]
      |  |-- †Nessariostoma granulosum Broili, 1933
      |  |-- †Paraplesiobatis heinrichsi Broili, 1933
      |  `-- †Pseudopetalichthys problematica Moy-Thomas, 1939 [Parapetalichthys Kuhn, 1949]
      |?- †Petalichthyida Jaeckel, 1911 [Petalichthyiformes]
      |?- †Phyllolepididae Agassiz, 1844 [Phyllolepida Stensiö, 1934]
      `--+--+-- †Acanthothoraci Stensiö, 1944
         |  `-- †Asterosteidae [Rhenanida Broili, 1930]
         `--+-- †Antiarchi Cope, 1885
            `--+-- †Ptyctodontidae Gross, 1932 [Ptyctodontida Gross, 1932]
               |-- †Arthrodira Woodward, 1891
               |-- †Entelognathus primordalis Zhu, Yu, Ahlberg, Choo, Lu, Qiao, Qu, Zhao, Jia, Blom & Zhu, 2013; L.Sil. EAs.
               `--o Eugnathostomata [paraphyletic Acanthodii Owen, 1846]
                  |==Diplacanthida Berg, 1940 [Diplacanthiformes Berg, 1940]
                  `--+-- †Ischnacanthiformes Berg, 1940
                     `--+==o Climatiida Berg, 1940
                        |  |-- †Gyracanthidae Woodward, 1906
                        |  |-- †Climatiidae Berg, 1940
                        |  `--+-- †Lupopsyrus pygmaeus Bernacsek & Dineley, 1977, E.Dev. WNNAm.
                        |     `-- Chondrichthyes Huxley, 1880 [Chondrichthiomorphi] (rustokalat; sharks & rays)
                        `--+-- †Acanthodiformes [Acanthodidae sensu Carroll, 1988]
                           `--o Osteichthyes Huxley, 1880 [Neoteleostomi] (bonefishes; luukalat)
                              |?-o †Lophosteus Pander, 1856 [Lophosteiformes Gross, 1969: †Lophosteidae Gross, 1969]
                              |  |-- †L. superbus Pander, 1856
                              |  |-- †L. connexus Märss, 1986
                              |  `-- †L. ohesaarensis Schultze & Märss, 2004
                              |?- †Naxilepis Wang & Dong, 1989
                              |-- Sarcopterygii Romer, 1955 (flesh-finned bonefishes, including tetrapods; lihaseväiset luukalat)
                              `-- Actinopterygii Klein, 1885 (non? Cope, 1887) (viuhkaeväiset luukalat; ray-finned bonefishes)


After Carroll, 1988, Nelson, 1994 and Zhu, Yu & Janvier, 1999

<==o Gnathostomata
   |?- †Placodermi
   `--+-- Chondrichthyes
      `--o Teleostomi
         |-- †Acanthodii
         `--o Osteichthyes
            `--+-- Sarcopterygii
               `-- Actinopterygii

Reference(s):