The Tetraodontiformes are an order of highly derived ray-finned fish, also called the Plectognathi. Sometimes these are classified as a suborder of the order Perciformes. The Tetraodontiformes are represented by 10 extant families and at least 349 species overall; most are marine and dwell in and around tropical coral reefs, but a few species are found in freshwater streams and estuaries. They have no close relatives, and descend from a line of coral-dwelling species that emerged around 80 million years ago.

Corals are marine invertebrates within the class Anthozoa of the phylum Cnidaria. They typically form compact colonies of many identical individual polyps. Coral species include the important reef builders that inhabit tropical oceans and secrete calcium carbonate to form a hard skeleton.

Hydrozoa are a taxonomic class of individually very small, predatory animals, some solitary and some colonial, most living in salt water. The colonies of the colonial species can be large, and in some cases the specialized individual animals cannot survive outside the colony. A few genera within this class live in fresh water. Hydrozoans are related to jellyfish and corals and belong to the phylum Cnidaria.

Anthozoa is a class of marine invertebrates which includes the sea anemones, stony corals and soft corals. Adult anthozoans are almost all attached to the seabed, while their larvae can disperse as part of the plankton. The basic unit of the adult is the polyp; this consists of a cylindrical column topped by a disc with a central mouth surrounded by tentacles. Sea anemones are mostly solitary, but the majority of corals are colonial, being formed by the budding of new polyps from an original, founding individual. Colonies are strengthened by calcium carbonate and other materials and take various massive, plate-like, bushy or leafy forms.

Opisthobranchs is now an informal name for a large and diverse group of specialized complex gastropods which used to be united in the subclass Opisthobranchia. That taxon is no longer considered to represent a monophyletic grouping.

Scleractinia, also called stony corals or hard corals, are marine animals in the phylum Cnidaria that build themselves a hard skeleton. The individual animals are known as polyps and have a cylindrical body crowned by an oral disc in which a mouth is fringed with tentacles. Although some species are solitary, most are colonial. The founding polyp settles and starts to secrete calcium carbonate to protect its soft body. Solitary corals can be as much as 25 cm (10 in) across but in colonial species the polyps are usually only a few millimetres in diameter. These polyps reproduce asexually by budding, but remain attached to each other, forming a multi-polyp colony of clones with a common skeleton, which may be up to several metres in diameter or height according to species.

Mussidae is a family of stony coral in the order Scleractinia. Following a taxonomic revision in 2012, the family is now restricted to species found in the Atlantic Ocean, with Pacific species transferred to the new family Lobophylliidae. Many species are referred to as brain coral because their generally spheroid form and grooved surface resembles the convolutions of a brain.

Alcyonacea, or soft corals, are an order of corals. In addition to the fleshy soft corals, the order Alcyonacea now contains all species previously known as "gorgonian corals", that produce a more or less hard skeleton, though quite different from "true" corals (Scleractinia). These can be found in suborders Holaxonia, Scleraxonia, and Stolonifera. They are sessile colonial cnidarians that are found throughout the oceans of the world, especially in the deep sea, polar waters, tropics and subtropics. Common names for subsets of this order are sea fans and sea whips; others are similar to the sea pens of related order Pennatulacea. Individual tiny polyps form colonies that are normally erect, flattened, branching, and reminiscent of a fan. Others may be whiplike, bushy, or even encrusting. A colony can be several feet high and across, but only a few inches thick. They may be brightly coloured, often purple, red, or yellow. Photosynthetic gorgonians can be successfully kept in captive aquaria.

Hexacorallia is a class of Anthozoa comprising approximately 4,300 species of aquatic organisms formed of polyps, generally with 6-fold symmetry. It includes all of the stony corals, most of which are colonial and reef-forming, as well as all sea anemones, and zoanthids, arranged within five extant orders. The hexacorallia are distinguished from another class of Anthozoa, Octocorallia, in having six or fewer axes of symmetry in their body structure; the tentacles are simple and unbranched and normally number more than eight. These organisms are formed of individual soft polyps which in some species live in colonies and can secrete a calcite skeleton. As with all Cnidarians, these organisms have a complex life cycle including a motile planktonic phase and a later characteristic sessile phase. Hexacorallia also include the significant extinct order of rugose corals.

Octocorallia is a subclass of Anthozoa comprising around 3,000 species of water-based organisms formed of colonial polyps with 8-fold symmetry. It includes the blue coral, soft corals, sea pens, and gorgonians within three orders: Alcyonacea, Helioporacea, and Pennatulacea. These organisms have an internal skeleton secreted by mesoglea and polyps with eight tentacles and eight mesentaries. As with all Cnidarians these organisms have a complex life cycle including a motile phase when they are considered plankton and later characteristic sessile phase.

Caryophylliina is a suborder of stony corals, order Scleractinia.

Although the phylogenetic classification of non-vertebrate animals remains a work-in-progress, the following taxonomy attempts to be useful by combining both traditional (old) and new (21st-century) paleozoological terminology.

Acroporidae is a family of small polyped stony corals in the phylum Cnidaria. The name is derived from the Greek "akron" meaning "summit" and refers to the presence of a corallite at the tip of each branch of coral. They are commonly known as staghorn corals and are grown in aquaria by reef hobbyists.

Astreopora is a genus of stony corals in the Acroporidae family. Members of the genus are commonly known as star corals and there are seventeen species currently recognized.

Pectiniidae was a family of stony corals, commonly known as chalice corals, but the name is no longer considered valid.

The Meandrinidae are a family of stony corals. The name comes from the Greek, maiandros meaning "meandering", referring to the miniature, winding valleys found between the corallites. Fossil corals in this family have been found dating back to the Cretaceous.

Stolonifera is a suborder of soft corals in the order Alcyonacea. Members of this taxon are characterised by having separate polyps budding off an encrusting horizontal, branching stolon. The skeletons include spicules or consists of a horny external cuticle. These soft corals are found in shallow tropical and temperate seas.

Oxypora glabra is a species of large polyp stony coral in the family Lobophylliidae. It is a colonial coral with thin encrusting laminae. It is native to the central Indo-Pacific.