So the paleobiologic systematics which follows is not intended to be all-inclusive or completely comprehensive. For practial reasons and relevancy, the below classification and annotations emphasize invertebrates that (a) are popularly collected as fossils and/or (b) no longer continue alive on this planet. Therefore, as a result, some phyla, classes, and orders of invertebrates are not listed.
If a non-vertebrate animal is mentioned below using its common, vernacular, everyday name, the creature is usually a living, present-day invertebrate. But if, on the other hand, a non-vertebrate is cited below by its scientific, taxonomic genus (in italics), then it is typically an extinct invertebrate, known only from the fossil record.
Invertebrate clades that are (a) very important as fossils (for example, ostracods frequently used as index fossils), and/or (b) very abundant as fossils (for example, crinoids easily found in crinoidal limestone), are highlighted with a bracketed exclamation mark [! ].
Invertebrate groups that (a) are now substantially extinct, and/or (b) contain a large proportion of extinct species, are followed by a dashed notation [-- such as this ]. But invertebrate clades which are now totally -- that is, 100 percent -- extinct are designated with a bracketed dagger/cross [† ]:
(opisthokonts / the animal-related kingdoms / the proto-spongal choanoflagellates, proto-fungal microsporidians, true fungi, and true animals
(parazoans / typically-sessile, basal non-eumetazoans / the most-primitive animals / the simplest, colonial, attached, bottom-dwelling, marine invertebrates)
(cone-shaped archaeocyathids/archeocyathids / cup-shaped archaeocyathans/archeocyathans / reef-building pleosponges / calcareous "ancient-cups")
(includes fossil genera such Archaeocyathus, Cambrocyathus, Atikonia, Tumuliolynthus, Kotuyicyathus, Metaldetes, Ajacicyathus and Paranacyathus)
(Archaeocyatha is sometimes classified as a class of Porifera below)
(quintessential true sponges / marine, colonial, pore-bearing animals / organized collar-flagellates / poriferans; today mostly siliceous) -- half of all documented species of Porifera are fossils and extinct
(Porifera may eventually be broken up into separate phyla)
(eumetazoans / true metazoans / typically-mobile, multicellular animals)
(Eumetazoa contains most of the living and deceased species of recorded life, including most invertebrates (alive and extinct), as well as all vertebrate animals)
(radiates / non-bilaterian eumetazoans)
(lophotrochozoan bilaterians, such as flatworms, ribbon worms, lophophorates, and molluscs)
(lampshells, brachiopods or "brachs," not to be confused with the hard-shelled marine mollusks below) -- 99 percent of all documented species of Brachiopoda are now extinct
(segmented worms such as earthworms and leeches)
(molluscs or mollusks, not to be confused with the hard-shelled marine brachiopods above)
(ecdysozoans, such as nematodes, horsehair worms, and molting bilaterians / panarthropods))
(panarthropodic water bears)
(panarthropodic velvet worms, including proto-arthropodic fossils of Arthropleura and Aysheaia)
(arthropods; jointed legged creatures with an exoskeleton)
(second-mouthed bilaterians called deuterostomians, such as chordates and echinoderms)
(echinoderms) -- 72 percent of all documented species of Echinodermata are fossils and extinct
(hemichordates such as extant acorn worms) -- Less than half of the documented species of Hemichordata are fossils and extinct
(both invertebrate and vertebrate chordates; animals possessing a notochord)