(i) Euteleostei
The euteleosts are the largest lineage within the teleosts and comprise some 375 families and over 18,000 species. There are four major radiations within the euteleosts usually recognized at the level of superorders:
1. Ostariophysi: about 6,000 species (dominate freshwaters of the world)
2. Protacanthopterygii: 300 species
3. Paracanthopterygii: 1,200 species
4. Acanthopterygii: 13,000 species (dominate marine environments)
Members of the ostariophysians and protacanthops appear to be related by the co-possession (by many, but not all lineages) of seemingly trivial traits such as:
1. an adipose fin
2. nuptial breeding tubercles
3. membraneous outgrowth of the first uroneural known as the "stegural" ("STEG" in the figure below. Note also the large number of hypurals - these become reduced to 2-3 hypural "plates" in higher teleosts).

4. lack of spines
5. abdominal position of pelvic fins
6. lack of jaw protrusion in protacanthops
(ii) The Ostariophysi
The ostariophysians are the first of the two major eutelost lineages (Acanthopterygi are the second). They dominate (75%) the composition of freshwater fishes and constitute about 25% of all known fishes. They predominate in the freshwaters of all continents except Australia (why??) and Antarctica.
The ostariophysians are satisfying to consider because they are one one the more coherent groups of fish based on the sharing of the following derived traits:
1. an alarm substance ("Schreckstoffen") that is released from the skin when flesh is broken (e.g., when bitten by a predator) and that elicits a "fright reaction" in all Ostariophysi
2. swimbladder subdivided into two lobes (see figure "10.3" below)
3. well developed breeding tubercles
Other characteristics that are usually found (but not exclusive) to ostariophysians are: abdominal position of pelvic fins, and adipose fin, and a highly protractile premaxillary bone (shaded bone in figure below).

The major orders within the ostariophysians are the Gonorhynchiformes, Cypriniformes, Characiformes, Siluriformes, and the Gymnotiformes. The latter four form a natural group (the "Otophysi") by the possession of a "Weberian apparatus".
The Weberian apparatus is a chain of bones that connects the inner ear with the swim bladder (much like the "otophysic connection" of the clupeoids) and is derived from the 4-5 anteriormost vertebrae (see figure).

The otophysi also have well developed "pharyngeal teeth" which are modifications of the branchial arches and provide a second, independent apparatus for food manipulation and processing.
Most otophysi are small fishes (i.e. less than 50 cm at maturity) although a few may reach 1-2 m in length. These attributes (modifications for sensory detection, fright response, protractile jaws, pharyngeal jaws, small size at maturity) likely have been very important in promoting diversity with the group. These attributes would seem to promote occupancy of a variety of niches and food resources as well as rapid response to environmental change via early ages at maturity.
Major orders of Ostariophysi:
A. Gonorhynchiformes: these are a small group (about 40 spp.) of largely freshwater fish (a few are brackish water or marine) that lack teeth on the jaws, have an epibranchial organ (for processing planktivorous prey), and have the first 3 vertebrae modified into what appears to be the precursory stage of the true Weberian apparatus. The best known member is the milkfish, Chanos chanos, which is one of the most important food fishes in Southeast Asia. The young are captured in nearshore marine environments and cultured in brackish water or salt water aquacultural ponds. Click HERE for more info.

B. Cypriniformes: this group of about 2700 species dominates the freshwaters of North America and Eurasia and consists of the "minnows", suckers, and loaches. These fishes all lack an adipose fin (differentiates them from the catfish and characins) and have highly protrusible upper jaws. They are really the first teleosts where the maxillary is completely excluded from the gape (see Cyprinus carpio above).
The major familes are the Cyprinidae (minnows), Catostomidae (suckers) and the loaches (Cobitidae). Although most cyprinds are characteristically small, one of the largest Ostariophysi is the Colorado squawfish (Ptychocheilus lucius) which can reach almost 2 m in length. The term "minnows", therefore, does not mean "small fish"! The Colorado squawfish is the focus of heavy conservation conservation effort in the highly impacted Colorado River basin.

Cyprinids are taxonomically most diverse in Southeast Asia, Africa and North America (where we have 270 species). They appear to be ecologically replaced by characins (see below) in South America where cyprinids are absent. Both are generally small-bodied generalist predators and there low degree of overlap might be driven, in part, by competitive exclusion.
An interesting group of cypriniformes includes the suckers, Catostomidae, which have a disjunct distribution. They probably had an origin in North America (there are about 70 species here), but there is one species in China as well.
These fishes are clearly specialized for exploiting the benthic habitats of lakes and streams with their subterminal mouths. There is, however, one North American genus (Chasmistes) which are mid-water planktivores with terminal mouths. Suckers are also quite interesting because they frequenctly hybridize and the family as a whole is thought to have arisen via genome duplications driven by hybridization between two ancestral taxa.
C. Characiformes: The charcins are a large (about 1200 species) of largely tropical ostariophysans that dominate the freshwaters of South America. A lower number (about 200) of species are found in Africa and a few make it into Central America, but only one (the Mexican tetra) makes it north to southwestern Texas (a classic example of a biogeographic filter effect) They have an adipose fin and usually have well developed teeth (in contrast to the cyprinids and catostomids). Most of the popular aquarium fishes that one see in NA are characins. Characins, strictly speaking, belong to a single family, the Characidae (but there are nine others in the order). One of the most famous, of course, is the piranha. Checkout this video of piranhas feeding (bird-lovers be warned!!). It is really quite remarkable, if a bit sensationalist in commentary.

Although piranhas are well known for their carnivory, characins as a group eat just about anything, including vegetation (including fruit), insects, fish, and fish scales!
D. Siluriformes: these are the catfishes, immediately recognizable by the one to four pairs of barbles on upper and lower jaws and the possession of an adipose fin. Catfishes also have a very much reduced to absent maxillary bone and may have a spine associated with the pectoral and/or dorsal fins. Catfish lack scales, but some have bony plates along the side of the body. Catfishes are very diverse (2400 species) and are known from all continents (including fossils in Antarctica), but reach their greatest diversity in South America (about 800 species). Catfishes are unique among the Otophysi as among the 34 families are two which are found in the marine habitat (the Ariidae and the Plotosidae). Both these marine familes also have freshwater relatives that likely represent secondary re-invasions of freshwater!
Of course, one of my personal favourite fishes is the pencil or parasitic catfishes, the Trichomycteridae of South America. One species, Vandellia cirrhosa (or "candiru") has been documented to swim up the urethra of bathers (it is attracted to currents) where it becomes well entrenched through the use of opercular spines, which requires surgical removal (ouch!).

The candiru is, therefore, the only known vertebrate parasite in humans. An "entertaining" account of candiru attacks and the ways in which people try to prevent them can be found in Gudger (1930).
Some of the largest freshwater fishes are also catfishes; the European catfish, Siluris glanis, which can reach 5 m in length!
More genrally, catfishes are interesting because they co-occur with both cyprinids (in North America and Eurasia) and characins (in South America and Africa), They may be able to co-exist with these other very diverse lineages because catfishes are primarily nocturnal and tend to exploit more benthic habitats. This way, catfishes and cyprinids/characins partition the habitat temporally as well as spatially which may promote their co-existence.
E. Gymnotiformes: the South/Central American knifefishes consist of about 60 species. They are best knowns for their ability to sense and generate electric currents (just like in the mormyrids and gymnarchids - both osteoglossomorphs). The most powerful electrical discharges in the order are produced by the electric "eels" (Electrophorus electricus). The electric eel is also well known for its ability to breath air through highly vascularized tissues in the mouth. Gymnotiforms also have a similar elongate body form to the African knifefishes (Notopteridae: Osteoglossomorpha). Hence, we have another example of convergence in electrosensitivity and body form between independently derived fish lineages.
References:
Briggs, JC. 1979. Ostariophysan zoogeography: an alternative
hypothesis.
Copeia 1979: 111-118.
Dauble, D.D. and R.L. Buschbom. 1981. Estimates of hybridization
between two species of catostomids in the Columbia River. Copeia
1981: 802-810.
Dimmick, W.W. and A. Larson. 1996. A molecular and morphological perspective on the phylogenetic relationships of the otophysan fishes. Mol. Phylogenetics Evol. 6: 120-133.
Gudger, E.W. 1930. On the alleged penetration of the human urethra by an Amozonian catfish called Candiru. Am. J. Surgery 8:170-189.
Pfeiffer, W. 1963. The fright reaction in North American fish. Can. J. Zool. 41: 69-77.
Sazima, I. and S. Guimaraes. 1987. Scavenging on human corpses as a source for stories about man-eating piranhas. En. Biol. Fishes 20: 75-77.