†Conodontophorida (otherwise an order according to Sepkoski, 2002)
Conodonts (Greekkōnos, "cone", + odont, "tooth") are extinct agnathanchordates resembling eels, classified in the class Conodonta. For many years, they were known only from tooth-like microfossils found in isolation and now called conodont elements. Knowledge about soft tissues remains limited. The animals are also called Conodontophora (conodont bearers) to avoid ambiguity.
Conodonts are considered index fossils, fossils used to define and identify geological periods.
Conodont elements from the Deer Valley Member of the Mauch Chunk Formation in Pennsylvania, Maryland, and West Virginia, USA
Figures 1, 2. Conodonts from the Deer Valley Member of the Mauch Chunk Formation, Keystone quarry, Pa. This collection (93RS–79c) is from the lower 10 cm of the Deer Valley Member. Note the nonabraded, although slightly broken, conodont elements of the high-energy oolitic marine facies of the Deer Valley Member. 1. Kladognathus sp., Sa element, posterior view, X140 2. Cavusgnathus unicornis, gamma morphotype, Pa element, lateral view, X140 3–9. Conodonts from the uppermost Loyalhanna Limestone Member of the Mauch Chunk Formation, Keystone quarry, Pa. This collection (93RS–79b) is from the upper 10 cm of the Loyalhanna Member. Note the highly abraded and reworked aeolian forms. 3, 4. Kladognathus sp., Sa element, lateral views, X140 5. Cavusgnathus unicornis, alpha morphotype, Pa element, lateral view, X140 6, 7. Cavusgnathus sp., Pa element, lateral view, X140 8. Polygnathus sp., Pa element, upper view, reworked Late Devonian to Early Mississippian morphotype, X140 9. Gnathodus texanus?, Pa element, upper view, X140 10–14. Conodonts from the basal 20 cm of the Loyalhanna Limestone Member of the Mauch Chunk Formation, Keystone quarry, Pa. (93RS–79a), and Westernport, Md. (93RS–67), note the highly abraded and reworked aeolian forms 10. Polygnathus sp., Pa element, upper view, reworked Late Devonian to Early Mississippian morphotype, 93RS–79a, X140 11. Polygnathus sp., Pa element, upper view, reworked Late Devonian to Early Mississippian morphotype, 93RS–67, X140 12. Gnathodus sp., Pa element, upper view, reworked Late Devonian(?) through Mississippian morphotype, 93RS–67, X140 13. Kladognathus sp., M element, lateral views, 93RS–67, X140 14. Cavusgnathus sp., Pa element, lateral view, 93RS–67, X140
Conodont teeth are the earliest found in the fossil record. The evolution of mineralized tissues has been puzzling for more than a century. It has been hypothesized that the first mechanism of mammalian tissue mineralization began either in the oral skeleton of conodont or the dermal skeleton of early agnathans.
The element array constituted a feeding apparatus that is radically different from the jaws of modern animals. They are now termed "conodont elements" to avoid confusion. The three forms of teeth, i.e., coniform cones, ramiform bars, and pectiniform platforms, probably performed different functions.
For many years, conodonts were known only from enigmatic tooth-like microfossils (200 micrometers to 5 millimeters in length), which occur commonly, but not always in isolation, and were not associated with any other fossil. Until the early 1980s, conodont teeth had not been found in association with fossils of the host organism, in a konservat lagerstätte. This is because the conodont animal was soft-bodied, thus everything but the teeth was unsuited for preservation under normal circumstances.
These microfossils are made of hydroxylapatite (a phosphatic mineral). The conodont elements can be extracted from rock using adequate solvents.
Model of elements of Manticolepis subrecta - a conodont from the Upper Frasnian of Poland - photography taken in the Geological Museum of the Polish Geological Institute in Warsaw
The conodont apparatus may comprise a number of discrete elements, including the spathognathiform, ozarkodiniform, trichonodelliform, neoprioniodiform, and other forms.
In the 1930s, the concept of conodont assemblages was described by Hermann Schmidt and by Harold W. Scott in 1934.
Elements of ozarkodinids
The feeding apparatus of ozarkodinids is composed at the front of an axial Sa element, flanked by two groups of four close-set elongate Sb and Sc elements which were inclined obliquely inwards and forwards. Above these elements lay a pair of arched and inward pointing (makellate) M elements. Behind the S-M array lay transversely oriented and bilaterally opposed (pectiniform, i.e. comb-shaped) Pb and Pa elements.
The "teeth" of some conodonts have been interpreted as filter-feeding apparatuses, filtering plankton from the water and passing it down the throat. Others have been interpreted as a "grasping and crushing array". The lateral position of the eyes makes it unlikely that conodonts were active predators. The preserved musculature suggests that some conodonts (Promissum at least) were efficient cruisers, but incapable of bursts of speed.
Milsom and Rigby envision them as vertebrates similar in appearance to modern hagfish and lampreys,
and phylogenetic analysis suggests they are more derived than either of these groups.
However, this analysis comes with one caveat: early forms of conodonts, the protoconodonts, appear to form a distinct clade from the later paraconodonts and euconodonts. Protoconodonts likely represent a stem group to the phylum that includes chaetognath worms; this conclusion suggests that chaetognaths are not close relatives of true conodonts.
Moreover, some analyses do not regard conodonts as either vertebrates or craniates, because they lack the main characteristics of these groups.
^Here, the hagfish are treated as a separate clade, as in Sweet and Donoghue's 2001 tree produced without cladistic analysis. However, it has been recognised by some  that the hagfish and lampreys may be closer to one another in their own clade, the Cyclostomata.
^Chemical systematics of conodont apatite determined by laser ablation ICPMS. Julie A. Trotter and Stephen M. Eggins, Chemical Geology, Volume 233, Issues 3–4, 15 October 2006, Pages 196–216, doi:10.1016/j.chemgeo.2006.03.004
^A Buffered Formic Acid Technique for Conodont Extraction. Lennart Jeppsson and Rikard Anehus, Journal of Paleontology, Vol. 69, No. 4 (Jul., 1995), pages 790-794 (Stable URL)
^Extraction Techniques for Phosphatic Fossils. Owen R. Green in A Manual of Practical Laboratory and Field Techniques in Palaeobiology. pages 318-330, doi:10.1007/978-94-017-0581-3_27
^Effects of extraction protocols on the oxygen isotope composition of conodont elements. Page C. Quinton, Stephen A. Leslie, Achim D. Herrmann and Kenneth G. MacLeod, Chemical Geology, Volume 431, 1 August 2016, Pages 36–43, doi:10.1016/j.chemgeo.2016.03.023
^Bergström, S. M.; Carnes, J. B.; Ethington, R. L.; Votaw, R. B.; Wigley, P. B. (1974). "Appalachignathus, a New Multielement Conodont Genus from the Middle Ordovician of North America". Journal of Paleontology. 48 (2): 227–235. Bibcode:1974JPal...48..524M. doi:10.2307/1303249 (inactive 2018-09-26). JSTOR1303249.
^Conodonten-Funde in ursprünglichem Zusammenhang. Hermann Schmidt, Paläontologische Zeitschrift, 1934, volume 16, Issue 1-2 , pages 76-85, doi:10.1007/BF03041668
^The Zoological Relationships of the Conodonts. Harold W. Scott, Journal of Paleontology, Vol. 8, No. 4 (Dec., 1934), pages 448-455 (Stable URL)
^Conodont Assemblages from the Heath Formation, Montana. Harold W. Scott, Journal of Paleontology, Vol. 16, No. 3 (May, 1942), pages 293-300 (Stable URL)
^Late Mississippian conodonts from the Bird Spring Formation in Nevada. David L. Dunn, Journal of Paleontology, November 1965, volume 39, issue 6 (abstract)
^A Questionable Natural Conodont Assemblage from Middle Ordovician Limestone, Ottawa, Canada. Christopher R. Barnes, Journal of Paleontology, Vol. 41, No. 6 (Nov., 1967), pages 1557-1560 (Stable URL)
^Bourlat, S. J; T. Juliusdottir, C. J Lowe, R. Freeman, J. Aronowicz, M. Kirschner, E. S Lander, M. Thorndyke, H. Nakano, A. B Kohn, others (2 November 2006). "Deuterostome phylogeny reveals monophyletic chordates and the new phylum Xenoturbellida". Nature. 444 (7115): 85–88. Bibcode:2006Natur.444...85B. doi:10.1038/nature05241. ISSN0028-0836. PMID17051155.CS1 maint: Multiple names: authors list (link)
^Sweet, W. C. (1988). "The Conodonta: morphology, taxonomy, paleoecology and evolutionary history of a long-extinct animal phylum". Oxford Monographs on Geology and Geophysics (10): 1–211.
Aldridge, R. J.; Briggs, D. E. G.; Smith, M. P.; Clarkson, E. N. K.; Clark, N. D. L. (1993). "The anatomy of conodonts". Philosophical Transactions of the Royal Society of London, Series B. 340 (1294): 405–421. doi:10.1098/rstb.1993.0082.