Acambona White, 1862 † (taxonomy source)
Acanthalosia Waterhouse, 1986 † (basis of record)
Acanthocosta Roberts, 1971 † (basis of record)
Acanthocrania Williams, 1943 † (basis of record)
Acanthospirifer Menakova, 1964 † (basis of record)
Acanthothirididae Schuchert, 1913 † (basis of record)
Acanthothiridinae Schuchert, 1913 † (basis of record)
Acrosaccus Willard, 1928 † (basis of record)
Acrospirifer Wedekind, 1926 † (basis of record)
Acrospiriferidae Termier & Termier, 1949 † (additional source)
Acrothelidae Schuchert, 1893 † (basis of record)
Acrotheloidea Walcott, 1908 † (basis of record)
Acrotreta Kutorga, 1848 † (basis of record)
Acrotretella Ireland, 1961 † (basis of record)
Acrotretida † (additional source)
Acrotretidae Schuchert, 1893 † (basis of record)
Acrotretoidea Schuchert, 1893 † (additional source)
Acutatheca Stainbrook, 1945 † (taxonomy source)
Adectorhynchinae Henry & Gordon, 1985 † (basis of record)
Adectorhynchus Henry & Gordon, 1985 † (additional source)
Adensuidae Popov & Rukavishnikova, 1986 † (basis of record)
Adnatidinae Williams et al., 2006 † (original description)
Adolfiidae Sartenaer, 1966 † (basis of record)
Adolfiinae Sartenaer, 1966 † (basis of record)
Adolfioidea Sartenaer, 1966 † (basis of record)
Adolfispirifer Krylova, 1962 † (basis of record)
Adreninae Boucot, 1994 † (basis of record)
Aemula Steinich, 1968 † (basis of record)
Aenigmastrophiidae Boucot & Rong, 1994 † (basis of record)
Aenigmathyris Cooper, 1971 † (basis of record)
Aetheia Thomson, 1915 † (additional source)
Aetheiinae Cooper, 1959 † (additional source)
Afilasma Stehli, 1961 † (additional source)
Afilasmatinae Williams et al., 2006 † (original description)
Agulhasiinae Muir-Wood, 1965 † (additional source)
Ahtiella Öpik, 1932 † (basis of record)
Ahtiellinae Öpik, 1933 † (basis of record)
Airtonia Cope, 1934 † (basis of record)
Airtoniinae Muir-Wood, 1962 † (basis of record)
Alabushevothyrididae Smirnova, 1994 † (basis of record)
Alabushevothyris Smirnova, 1994 † (additional source)
Aldingia Thomson, 1916 (additional source)
Alisina Rowell, 1962 † (additional source)
Allanetes Boucot & Johnson, 1967 † (taxonomy source)
Allorhynchidae Cooper & Grant, 1976 † (additional source)
Almorhynchia Ovtsharenko, 1983 † (basis of record)
Altiplecus Stehli, 1954 † (additional source)
Ambocoeliidae George, 1931 † (basis of record)
Ambocoeliinae George, 1931 † (basis of record)
Ambocoelioidea George, 1931 † (basis of record)
Ambothyris George, 1931 † (basis of record)
Amphipellidae Cooper & Grant, 1976 † (additional source)
Amphistrophiidae Harper, 1973 † (basis of record)
Anastrophia Hall, 1867 † (additional source)
Anazygidae Davidson, 1883 † (basis of record)
Anazygidina † (basis of record)
Anazyginae Davidson, 1883 † (basis of record)
Anazygoidea Davidson, 1883 † (basis of record)
Ancillotoechia Havliček, 1959 † (additional source)
Ancistrorhynchidae Cooper, 1956 † (basis of record)
Ancistrorhynchoidea Cooper, 1956 † (basis of record)
Ancorellininae Baker & Mancenido, 1997 † (additional source)
Anemonaria Cooper & Grant, 1969 † (additional source)
Angusticardinia Schuchert & Cooper, 1931 † (basis of record)
Angusticardiniidae Schuchert & Cooper, 1931 † (basis of record)
Angustothyrididae Dagys, 1972 † (basis of record)
Aniabrochinae Mancenido, 1993 † (basis of record)
Anidanthinae Waterhouse, 1968 † (basis of record)
Anisopleurella Cooper, 1956 † (additional source)
Anomalorthidae Ulrich & Cooper, 1936 † (basis of record)
Anomalorthis Ulrich & Cooper, 1936 † (additional source)
Anoplia Hall & Clarke, 1892 † (basis of record)
Anopliidae Muir-Wood, 1962 † (basis of record)
Anopliinae Muir-Wood, 1962 † (basis of record)
Anopliopsis Girty, 1938 † (additional source)
Anoplothecidae Schuchert, 1894 † (basis of record)
Anoplothecoidea Schuchert, 1894 † (basis of record)
Anoptambonites Williams, 1962 † (additional source)
Antronaria Cooper & Grant, 1976 † (additional source)
Antzeilleridae Xu & Liu, 1983 † (basis of record)
Aorhynchia MacFarlan, 1992 † (additional source)
Aparimarhynchia MacFarlan, 1992 † (taxonomy source)
Apatobolus Popov in Nazarov & Popov, 1980 † (additional source)
Apatomorpha Cooper, 1956 † (additional source)
Aperispirifer Waterhouse, 1968 † (taxonomy source)
Aphaurosia Cooper & Grant, 1976 † (additional source)
Aphelesiinae Cooper, 1959 † (additional source)
Aporthophyla Ulrich & Cooper, 1936 † (taxonomy source)
Apringia Gregorio, 1886 † (basis of record)
Araksalosiidae Lazarev, 1989 † (basis of record)
Araksalosiinae Lazarev, 1989 † (basis of record)
Araratella Abramian, Plodowski & Sartenaer, 1975 † (additional source)
Araratellinae Erlanger, 1986 † (basis of record)
Archaeorthidae Williams & Harper in Williams et al., 2007 † (original description)
Archboldina Waterhouse, 2001 † (additional source)
Arcticalosia Waterhouse, 1986 † (additional source)
Arctitreta Whitfield, 1908 † (basis of record)
Areostrophiidae Manankov, 1979 † (basis of record)
Areostrophiinae Manankov, 1979 † (additional source)
Artiotreta Ireland, 1961 † (basis of record)

 Taxonomic remark

 for Athyridida †

Per the Treatise on Invertebrate Paleontology (Williams et al (2002), revised volume 4, Rhynchonelliformea (part)), ... [details]

 Taxonomic remark

 for Cruralina Smirnova, 1966 †

Genus originally placed in the sub-family Cancellothyrinae (Family Cancellothyrididae), but in Williams et al. ... [details]

 Taxonomic remark

 for Dolerorthidae Öpik, 1934 †

Family Dolerorthidae frequently split into two subfamilies (Dolerorthinae and Hesperorthinae). However ... [details]

 Taxonomic remark

 for Draciinae Steinich, 1967 †

Draciinae was allocated to family Chlidonophoridae by the Treatise (Williams et al., 2006). Draciinae was ... [details]

 Taxonomic remark

 for Hercothyrididae Cooper, 1979 †

Cooper (1979) created the family Hercothyrididae to accommodate Hercothyris (the type genus) and also Dallina, ... [details]

 Taxonomic remark

 for Hypopsia Cooper & Grant, 1974 †

Originally placed by Cooper & Grant (1974) in family Schuchertellidae, sub-family Hypopsiinae. Williams et al. ... [details]

 Taxonomic remark

 for Hypopsiinae Cooper & Grant, 1974 †

Genus Hypopsia was originally placed by Cooper & Grant (1974) in family Schuchertellidae, sub-family Hypopsiinae. ... [details]

 Taxonomic remark

 for Pegmathyris Hatai, 1938 †

Originally described by Hatai as a subgenus of Dallina, but recognized at the genus level by the most recent ... [details]

 Taxonomic remark

 for Sinopunctatrypa Yu, Copper & Jia-Yu, 1983 †

Created as a subgenus of Punctatrypa, later elevated to genus level in Treatise on Invertebrate Paleontology. [details]

 Taxonomic remark

 for Soaresirhynchia Alméras, 1994 †

The 2002 Treatise on Invertebrate Paleontology moved this genus to subfamily Basiliolinae of Basiliolidae ... [details]