Note: this is not meant to be an exhaustive list. Only some examples are given at some taxonomic levels.

SUPERCLASS Agnatha: Jawless vertebrates (all are fish)

• CLASS Cephalaspidomorpha
  • ORDER Petromyzoniformes: Lampreys
  • ORDER Osteostraci: extinct heavily armored agnathans.
• CLASS Myxini: hagfishes

SUPERCLASS Gnathostomata: Vertebrates with jaws, including fish.

• GRADE Placodermiomorphi
  • CLASS Placodermi: extinct armored jawed fish
• GRADE Chondricthiomorphi
  • CLASS Chondrichthyes: cartilagenous fish
    • SUBCLASS Elasmobranchii: slitlike gill openings.
      • SUPERORDER Cladoselachimorpha: Primative extinct sharks of the Devonian to Pennsylvanian
      • SUPERORDER Euselacii (modern sharks, rays)
        • ORDER Squaliformes: Squalus
        • ORDER Lamniformes: Great White shark
        • ORDER Orectolobiformes: Whale sharks (world's largest fish)
        • ORDER Rajiformes:Sawfish, skates, rays
    • SUBCLASS Holocephali: Chimaera (ratfish).
• GRADE Teleostomi: bony fish
  • CLASS Acanthodii: Extinct bony fish of the Silurian and Permian
  • CLASS Actinopterygii: ray-finned fishes
    • SUBCLASS Chondrostei: primative ray-finned fish: sturgeons, paddlefish, bichirs.
    • SUBCLASS Neopterygii: modern ray-finned fish: gars, bowfins, "teleosts".

      • ORDER Semionotiformes: gars
      • ORDER Amiiformes: bowfins

      DIVISION Teleostei: advanced neopterygians.

      • SUBDIVISION Elopomorpha: Tarpons and eels
        • ORDER Elopoformes: Tarpons
        • ORDER Anguilliformes: eels
      • SUBDIVISION Clupeomorpha: herrings and relatives
      • SUBDIVISION Osteoglossomorpha: African elephant fish.
      • SUBDIVISION Euteleosti. Poorly-defined group of modern fish.
        • SUPERORDER Protoacanthopterygii. Salmon, trout, pike
        • SUPERORDER Ostariophysi: carp, catfish, minnows, knifefish
        • SUPERORDER Stenopterygii
          • ORDER Stomatiiformes: light fishes
        • SUPERORDER Cyclosquamata
          • SUBFAMILY Harpadontinae: bombay ducks
          • FAMILY Paralepididae: barracudas
        • SUPERORDER Scopelomorpha: lantern fish
        • SUPERORDER Paracanthopterygii: perch, cod
        • SUPERORDER Acanthopterygii: seahorses, sculpins, bass, halibut, perch and many others.

  • CLASS Sarcopterygii: fleshy-finned fishes and tetrapods.
    • SUBCLASS Coelacanthimorpha
      • ORDER Coelacanthiformes: Latimeria chalumnae
    • SUBCLASS Dipnoi and Porolipimorpha
      • INFRACLASS Dipnoi: Lungfishes
    • SUBCLASS Rhizodontiformes: extinct fish, sister group to tetrapods.
    • SUBCLASS Osteolepimorpha: Rhipidistans.. Extinct primative freshwater fish. Probable ancestors of tetrapods. Strongly resemble labrynthodonts in teeth and skull structure.
    • SUBCLASS Tetrapoda: tetrapod craniates. Amphibia and Amniota.

Nelson, Joseph S. (1994). Fishes of the World (3rd ed.). J. Wiley and Sons, Canada.

Skin	Jawless fish: smooth epidermis. Jawed fish: scales of dermal origin. Elasmobranchs have dermal denticles. Teleosts have a variety of scale types.
Head skeleton	Jawless fishes: cartilagenous. Visceral (pharyngeal) skeleton and chondrocranium a single unit. Jawed fishes: First gill arch becomes jaws. Cartilagenous fish have single cranial capsule. Bony fish have many and varied cranial bones.
Skeleton	Jawless fishes: chondrocranium and visceral skeleton only. Nonossified. Notochord persists. Chondrichthyes: Skeleton nonossified. Pelvic and pectoral girdles. Vertebral column. Bony fishes:Skeleton ossified.
Fins	Agnathans: No trace of paired fins. Chondrycthyes: paired fins supported by cartilagenous rays Actinopterygii: paired fins supported by bony rays. Sarcopterygii: paired fins have fleshy bases, thicker bones. Fins gave rise to tetrapod fins.
Muscles	Segmental myomeres. More complicated in structure in teleosts, but basically W or chevron shaped. In jawed fishes, specialized muscles control jaws, fins.
Digestive System	Cyclostomes: relatively undifferentiated gut from intestine to anus. Sharks and rays have spiral valve instead of intestine.
Respiration	All fish external respiration is by gills. Cyclostomes use pharyngeal pouches. First pharyngeal pouch of cyclostomes becomes spiracle in elasmobranchs (and middle ear in tetrapods). Countercurrent exchange is seen in all fish gills. Osteichthyes use opercular pump for continuous flow.
Gas Bladders and Lungs	Bony fish have gas bladders derived from the gut. In teleosts and most other marine fish the canal to the gut is closed (physoclistous condition), but in lungfish it is open (physostomous). Generally supplied by the celiacomesenteric artery which comes from the dorsal aorta. Lungfish have developed a pulmonary artery. Bladder also used as resonator in both sound production and sound detection.
Heart	Two main chambers: atrium and ventrical. A sinus venosus is usually present and ranges from prominent (sharks) to insignificant (cyclostomes). A conus arteriosus is also usually present and also varies in size from large and muscular (cartilagenous fish) to virtually absent (cyclostomes, teleosts). Lungfish heart is called "intermediate" in that there is some separation of oxygenated and deoxygenated blood.
Circulatory system	Typically vertebrate except that: cyclostomes have a very primative lymph system which carries some red blood cells. The lymph system is also incomplete in Dipnoi (lungfish) but fully developed in Neopterygii.
Kidneys	Mesonephric or opishonephric kidneys (some pronephros in larvae). Nephric tubules generally (though not always) consist of coelom-derived renal capsules containing a tuft of capillaries called a glomerulus (capsule and glomerulus are the renal corpuscle). Nephron has a proximal convoluted tubule, an intermediate segment, and a distal convoluted tubule which discharges into a nephric duct which empties into a cloaca.
Nervous system	Typical vertebrate: myelinated nerves, dorsal hollow spinal cord, biramous spinal nerves, brain divided into hindbrain (medulla), midbrain (pons, tectum) and forebrain (olfactory lobes).
Special senses	Electroreception (elasmobranchs and some teleosts); lateral line.