In the 10th edition of Systema Naturae, Carl Linnaeus described the Pisces as:^[1]

Always inhabiting the waters; are swift in their motion and voracious in their appetites. They breathe by means of gills, which are generally united by a bony arch; swim by means of radiate fins, and are mostly covered over with cartilaginous scales. Besides the parts they have in common with other animals, they are furnished with a nictitant membrane, and most of them with a swim-bladder, by the contraction or dilatation of which, they can raise or sink themselves in their element at pleasure.

Linnaean Characteristics^[1]

• Heart: 1 auricle, 1 ventricle. Cold, dark red blood
• Gills: external
• Jaw: incumbent
• Penis: (usually) none
• Eggs: without whites
• Organs of Sense: tongue, nostrils?, eyes, ears
• Covering: imbricate scales
• Supports: fins. Swims in the Water & Smacks.

Apodes

Muraena (eels)

• Muraena helena – Mediterranean moray
• Muraena ophis – Spotted snake eel
• Muraena serpens – Serpent eel
• Muraena anguilla – European eel
• Muraena myrus – Painted eel
• Muraena conger – European conger
• Muraena caeca – European finless eel

Gymnotus (electric knifefishes)

• Gymnotus carapo – Banded knifefish
• Gymnotus asiaticus – Snakehead

Trichiurus (cutlassfishes)

• Trichiurus lepturus – Largehead hairtail

Anarhichas (wolffishes)

• Anarhichas lupus – Atlantic wolffish

Ammodytes (sand eels)

• Ammodytes tobianus – Lesser sand eel

Stromateus (butterfishes)

• Stromateus fiatola – Blue Butterfish
• Stromateus paru – American Harvestfish

Xiphias (swordfishes)

• Xiphias gladius – Swordfish

Jugulares

Callionymus (dragonets)

• Callionymus lyra & Callionymus dracunculus – Common Dragonet
• Callionymus indicus – Bartail flathead

Uranoscopus (stargazers)

• Uranoscopus scaber – Uranoscopus scaber

Trachinus (weevers)

• Trachinus draco – Greater weever

Gadus (cod & kin)

• Gadus aeglefinus – Haddock
• Gadus morhua & Gadus callarias – Atlantic Cod
• Gadus luscus & Gadus barbatus – Pouting
• Gadus minutus – Poor cod
• Gadus virens & Gadus carbonarius – Coalfish
• Gadus merlangus – Whiting
• Gadus pollachius – Pollock
• Gadus merluccius – European hake
• Gadus molva – Common ling
• Gadus lota – Burbot
• Gadus mustela – Fivebeard rockling
• Gadus mediterraneus – Shore rockling

Blennius (blennies)

• Blennius galerita – Montagu's blenny
• Blennius cristatus – Molly Miller
• Blennius cornutus – Horned blenny
• Blennius ocellaris – Butterfly Blenny
• Blennius gattorugine – Tompot blenny
• Blennius superciliosus – Clinus superciliosus
• Blennius mustelarius – nomen dubium
• Blennius pholis – Combtooth blenny
• Blennius gunnellus – Rock gunnel
• Blennius viviparus – Viviparous eelpout
• Blennius lumpenus – unknown
• Blennius raninus – Tadpole fish

Ophidion (cusk-eels)

• Ophidion barbatum – Snake blenny
• Ophidion imberbe – Rock gunnel
• Ophidion macrophthalmum – Red bandfish

Thoracici

Cyclopterus

Cyclopterus (Lumpfishes)

• Cyclopterus lumpus – Cyclopterus lumpus
• Cyclopterus nudus – Gobiesox nudus

Echeneis

Echeneis (Remoras)

• Echeneis remora – Common remora
• Echeneis neucrates – Live sharksucker

Coryphaena

Coryphaena (Dolphinfishes)

• Coryphaena hippurus – Common dolphinfish
• Coryphaena equiselis – Pompano dolphinfish
• Coryphaena pentadactyla – Fivefinger wrasse
• Coryphaena novacula – Pearly razorfish
• Coryphaena pompilus – Rudderfish

Gobius

Gobius (Gobies)

• Gobius niger & Gobius jozo – Black goby
• Gobius paganellus – Rock goby
• Gobius eleotris
• Gobius aphya
• Gobius pectinirostris – Blue-spotted mud hopper
• Gobius anguillaris – Taenioides anguillaris

Cottus

Cottus (Sculpins)

• Cottus cataphractus – Agonus cataphractus
• Cottus quadricornis – Fourhorn sculpin
• Cottus grunniens – Allenbatrachus grunniens
• Cottus scaber – Grammoplites scaber
• Cottus scorpius – Shorthorn sculpin
• Cottus gobio – European bullhead

Scorpaena

Scorpaena (Scorpionfishes)

• Scorpaena porcus – European scorpionfish
• Scorpaena scrofa – Bigscale scorpionfish

Zeus

Zeus (John Dories & kin)

• Zeus vomer – Lookdown
• Zeus gallus – Selene gallus
• Zeus faber – John Dory
• Zeus aper – Capros aper

Pleuronectes

Pleuronectes (Flatfishes)

• Pleuronectes achirus – Achirus achirus
• Pleuronectes trichodactylus – Monochirus trichodactylus
• Pleuronectes lineatus – Lined sole
• Pleuronectes ocellatus – Microchirus ocellatus
• Pleuronectes lunatus – Plate fish
• Pleuronectes hippoglossus – Atlantic halibut
• Pleuronectes cynoglossus – Trobay sole
• Pleuronectes platessa – European plaice
• Pleuronectes flesus & Pleuronectes passer – European flounder
• Pleuronectes limanda – Common dab
• Pleuronectes solea – Common sole
• Pleuronectes linguatula – Citharus linguatula
• Pleuronectes rhombus – Brill
• Pleuronectes maximus – Turbot
• Pleuronectes papillosus – Syacium papillosum

Chaetodon

Chaetodon (Butterflyfishes, Angelfishes, & kin)

• Chaetodon canescens & Chaetodon cornutus – Moorish idol
• Chaetodon argenteus – Silver moony
• Chaetodon acuminatus & Chaetodon macrolepidotus – Pennant coralfish
• Chaetodon pinnatus – Dusky batfish
• Chaetodon punctatus – Drepane punctata
• Chaetodon arcuatus – Gray angelfish
• Chaetodon rostratus – Copperband butterflyfish
• Chaetodon nigricans – Acanthurus nigricans
• Chaetodon triostegus – Convict surgeonfish
• Chaetodon lineatus – Striped surgeon
• Chaetodon striatus – Banded butterflyfish
• Chaetodon aruanus – Whitetail dascyllus
• Chaetodon capistratus – Foureye butterflyfish
• Chaetodon vagabundus – Vagabond butterflyfish
• Chaetodon ciliaris – Queen angelfish
• Chaetodon saxatilis – Sergeant major
• Chaetodon rotundus – Abudefduf septemfasciatus
• Chaetodon lanceolatus – Jack-knifefish

Sparus

Sparus (Breams and Porgies)

• Sparus aurata – Gilt-head bream
• Sparus annularis – Diplodus annularis
• Sparus sargus – Diplodus sargus
• Sparus melanurus – Saddled seabream
• Sparus smaris – Spicara smaris
• Sparus maena – Spicara maena
• Sparus saxatilis – Crenicichla saxatilis
• Sparus orphus & Sparus pagrus – Red porgy
• Sparus hurta & Sparus mormyrus – Lithognathus mormyrus
• Sparus erythrinus – Common pandora
• Sparus boops – Boops boops
• Sparus cantharus – Black seabream
• Sparus chromis – Chromis chromis
• Sparus salpa – Salema porgy
• Sparus synagris – Lane snapper
• Sparus dentex – Common dentex
• Sparus spinus – Siganus spinus
• Sparus virginicus – Porkfish
• Sparus capistratus
• Sparus galilaeus – Mango tilapia

Labrus

Labrus (Wrasses, Parrotfishes, & kin)

• Labrus scarus
• Labrus cretensis – Mediterranean parrotfish
• Labrus anthias – Anthias anthias
• Labrus hepatus – Serranus hepatus
• Labrus griseus – Mangrove snapper
• Labrus lunaris – Moon wrasse
• Labrus opercularis – Paradise fish
• Labrus pavo – Ornate wrasse
• Labrus auritus – Redbreast sunfish
• Labrus falcatus – Permit
• Labrus rufus – Spanish hogfish
• Labrus marginalis
• Labrus ferrugineus
• Labrus julis & Labrus paroticus – Mediterranean rainbow wrasse
• Labrus suillus & Labrus rupestris – Goldsinny wrasse
• Labrus striatus – Black sea bass
• Labrus gvaza – Venezuelan grouper
• Labrus ocellaris
• Labrus tinca – Symphodus tinca
• Labrus bimaculatus – Cichlasoma bimaculatum
• Labrus punctatus – Polycentrus schomburgkii
• Labrus melops – Corkwing wrasse
• Labrus niloticus – Nile perch
• Labrus ossifagus, Labrus mixtus, & Labrus varius – Cuckoo wrasse
• Labrus onitis – Tautog
• Labrus viridis – Green wrasse
• Labrus luscus – Green wrasse
• Labrus livens – Labrus merula
• Labrus turdus – Labrus viridis
• Labrus exoletus & Labrus chinensis – Centrolabrus exoletus
• Labrus linearis
• Labrus fulvus – Cephalopholis fulva
• Labrus radiatus – Puddingwife wrasse
• Labrus merula – Brown wrasse
• Labrus cynaedus

Sciaena

Sciaena (Snappers & Croakers)

• Sciaena cappa
• Sciaena lepisma
• Sciaena unimaculata
• Sciaena umbra – Brown meagre
• Sciaena cirrosa – Umbrina cirrosa

Perca

Perca (Perch, Grouper, & kin)

• Perca fluviatilis – European perch
• Perca lucioperca – Zander (Sander lucioperca)
• Perca asper – Asper (Zingel asper)
• Perca labrax – European seabass (Dicentrarchus labrax)
• Perca nilotica – Nile tilapia (Oreochromis niloticus)
• Perca marina – Painted comber (Serranus scriba)
• Perca nobilis – Barred grunt (Conodon nobilis)
• Perca polymna – Saddleback clownfish (Amphiprion polymnus)
• Perca cottoides – Marbled stingfish (Cottapistus cottoides)
• Perca philadelphica – Centropristis philadelphica
• Perca mediterranea – Axillary wrasse (Symphodus mediterraneus)
• Perca vittata – Oriental Sweetlips (Plectorhinchus vittatus)
• Perca punctata – Coney (Cephalopholis fulva)
• Perca guttata – Red hind (Epinephelus guttatus)
• Perca scriba – Painted comber (Serranus scriba)
• Perca venenosa – Yellowfin grouper (Mycteroperca venenosa)
• Perca melanura – Cottonwick grunt (Haemulon melanurum)
• Perca gibbosa – Pumpkinseed (Lepomis gibbosus)
• Perca saltatrix – Kyphosus sectatrix
• Perca stigma
• Perca diagramma – Striped sweetlips (Plectorhinchus diagrammus)
• Perca striata – Striped grunt (Haemulon striatum)
• Perca lineata – Yellowbanded sweetlips (Plectorhinchus lineatus)
• Perca rhomboidalis – Western Atlantic seabream (Archosargus rhomboidalis)
• Perca cernua – Ruffe (Gymnocephalus cernua)
• Perca schraetser – Striped ruffe Gymnocephalus schraetser
• Perca argentea – Terapon theraps
• Perca cabrilla – Comber (Serranus cabrilla)
• Perca radula

Gasterosteus

Gasterosteus (Sticklebacks & kin)

• Gasterosteus aculeatus – Three-spined stickleback
• Gasterosteus ductor – Pilot fish
• Gasterosteus occidentalis
• Gasterosteus ovatus – Trachinotus ovatus
• Gasterosteus pungitius – Ninespine stickleback
• Gasterosteus volitans – Red lionfish
• Gasterosteus spinachia – Spinachia spinachia
• Gasterosteus spinarella – Flying gurnard

Scomber

Scomber (Mackerel & Tuna)

• Scomber scombrus – Atlantic mackerel
• Scomber pelamis – Skipjack tuna
• Scomber thynnus – Atlantic bluefin tuna
• Scomber cordyla – Torpedo scad
• Scomber glaucus – Trachinotus ovatus
• Scomber trachurus – Atlantic horse mackerel
• Scomber amia – Lichia amia
• Scomber pelagicus – Dolphinfish

Mullus

Mullus (Goatfishes)

• Mullus barbatus – Bluntsnouted mullet
• Mullus surmuletus – Red mullet
• Mullus imberbis – Cardinalfish

Trigla

Trigla (Sea robins)

• Trigla cataphracta – Peristedion cataphractum
• Trigla lyra – Piper gurnard
• Trigla gurnardus – Grey gurnard
• Trigla cuculus – East Atlantic red gurnard
• Trigla lucerna – Tub Gurnard
• Trigla hirundo – Chelidonichthys gabonensis
• Trigla asiatica
• Trigla volitans – Flying gurnard

Abdominales

Cobitis (Loaches)

• Cobitis anableps – Four-eyed fish
• Cobitis barbatula – Stone loach
• Cobitis taenia – Spined loach
• Cobitis fossilis – European weatherfish

Silurus (Catfishes)

• Silurus asotus – Amur catfish
• Silurus glanis – Wels catfish
• Silurus aspredo – Aspredo aspredo
• Silurus mystus – African Butter catfish
• Silurus anguillaris – Mudfish
• Silurus batrachus – Walking catfish
• Silurus undecimalis
• Silurus militaris – Osteogeneiosus militaris
• Silurus catus – White catfish
• Silurus clarias – Synodontis clarias
• Silurus ascita
• Silurus costatus – Platydoras costatus
• Silurus callichthys – Armored catfish
• Silurus cataphractus – Acanthodoras cataphractus

Loricaria (Suckermouth Catfishes)

• Loricaria cataphracta – Suckermouth catfish

Salmo (Salmon, Trout, & kin)

• Salmo salar – Atlantic salmon
• Salmo eriox, Salmo trutta, Salmo fario, & Salmo lacustris – Brown trout
• Salmo hucho – Huchen
• Salmo carpio – Carpione
• Salmo alpinus – Arctic char
• Salmo salvelinus, Salmo salmarinus, & Salmo umbla – Salvelinus umbla
• Salmo eperlanus – European smelt
• Salmo saurus – Atlantic lizardfish
• Salmo lavaretus – Common whitefish
• Salmo albula & Salmo vimba – Vendace
• Salmo thymallus – Grayling
• Salmo oxyrinchus – Houting
• Salmo gibbosus – Charax gibbosus
• Salmo bimaculatus – Astyanax bimaculatus
• Salmo immaculatus – Curimata cyprinoides
• Salmo niloticus – nomen dubium
• Salmo pulverulentus – Acestrorhynchus falcatus
• Salmo anostomus – Anostomus anostomus

Fistularia (Cornetfishes)

• Fistularia tabacaria – Bluespotted cornetfish

Esox (Pike, Gar, and kin)

• Esox sphyraena – European barracuda
• Esox osseus – Longnose gar
• Esox vulpes – Bonefish
• Esox synodus – Diamond lizardfish
• Esox lucius – Northern pike
• Esox hepsetus – Anchoa hepsetus
• Esox bellone
• Esox brasiliensis – Ballyhoo
• Esox gymnocephalus – unknown

Argentina (Herring smelts)

• Argentina sphyraena – European argentine

Atherina (Silversides)

• Atherina hepsetus – Mediterranean sand smelt

Mugil (Mullet)

• Mugil cephalus – Flathead mullet

Exocoetus (Flying fishes)

• Exocoetus volitans – Tropical two-winged flying fish

Polynemus (Threadfins)

• Polynemus quinquarius – Pentanemus quinquarius
• Polynemus virginicus – Polydactylus virginicus
• Polynemus paradiseus – Paradise threadfin

Clupea (Herring, Hatchetfishes, & kin)

• Clupea harengus – Atlantic herring
• Clupea sprattus – European sprat
• Clupea alosa – Allis shad
• Clupea encrasicolus – European anchovy
• Clupea thrissa – Clupanodon thrissa
• Clupea sima
• Clupea sternicla – Common hatchetfish
• Clupea mystus – Coilia mystus
• Clupea tropica
• Clupea sinensis – Tenualosa reevesii

Cyprinus (Carp & kin)

• Cyprinus barbus – Common barbel
• Cyprinus carpio – Common carp
• Cyprinus gobio – Gobio gobio
• Cyprinus americanus – Menticirrhus americanus
• Cyprinus carassius – Crucian carp
• Cyprinus tinca – Tench
• Cyprinus cephalus – European chub
• Cyprinus auratus – Goldfish
• Cyprinus niloticus
• Cyprinus phoxinus & Cyprinus aphya – Common minnow
• Cyprinus leuciscus, Cyprinus dobula, & Cyprinus grislagine – Common dace
• Cyprinus idbarus, Cyprinus idus, Cyprinus orfus, & Cyprinus jeses – Ide
• Cyprinus rutilus – Common roach
• Cyprinus erythrophthalmus – Common rudd
• Cyprinus nasus – Common Nase
• Cyprinus aspius – Asp
• Cyprinus alburnus – Common Bleak
• Cyprinus vimba – Vimba bream
• Cyprinus dentex – Alestes dentex
• Cyprinus brama – Carp bream
• Cyprinus cultratus – Ziege
• Cyprinus bjoerkna – Silver bream
• Cyprinus farenus & Cyprinus ballerus – Blue bream

Branchiostegi

Mormyrus (Elephantfishes)

• Mormyrus cyprinoides – Marcusenius cyprinoides
• Mormyrus anguilloides – Cornish jack
• Mormyrus caschive – Mormyrus caschive

Balistes (Triggerfishes)

• Balistes monoceros – Unicorn leatherjacket
• Balistes tomentosus – Acreichthys tomentosus
• Balistes papillosus – Papillose filefish
• Balistes verrucosus – Rhinecanthus verrucosus
• Balistes aculeatus – Lagoon triggerfish
• Balistes vetula – Queen triggerfish
• Balistes ringens – Xanthichthys ringens
• Balistes scolopax – Longspine snipefish

Ostracion (Boxfishes & Cowfishes)

• Ostracion triqueter – Lactophrys triqueter
• Ostracion trigonus – Lactophrys trigonus
• Ostracion bicaudalis – Spotted trunkfish
• Ostracion tricornis & Ostracion quadricornis – scrawled cowfish
• Ostracion cornutus – longhorn cowfish
• Ostracion tuberculatus & Ostracion cubicus – yellow boxfish
• Ostracion gibbosus – Tetrosomus gibbosus

Tetraodon (Pufferfishes & Sunfishes)

• Tetraodon testudineus – Checkered puffer
• Tetraodon lagocephalus – Oceanic puffer
• Tetraodon lineatus – Fahaka pufferfish
• Tetraodon ocellatus – Takifugu ocellatus
• Tetraodon hispidus – White-spotted puffer
• Tetraodon mola – Ocean sunfish

Diodon (Porcupinefishes)

• Diodon atringa – Chilomycterus atringa
• Diodon reticulatus & Diodon echinatus – Chilomycterus reticulatus
• Diodon spinosus – Chilomycterus spinosus
• Diodon hystrix – Spot-fin porcupinefish
• Diodon holocanthus – Long-spine porcupinefish
• Diodon raninus

Centriscus (Shrimpfishes)

• Centriscus scutatus – Grooved shrimpfish

Syngnathus (Pipefishes & Seahorses)

• Syngnathus typhle – Broad-nosed pipefish
• Syngnathus acus – Common pipefish
• Syngnathus pelagicus – Pelagic pipefish
• Syngnathus aequoreus – Entelurus aequoreus
• Syngnathus ophidion & Sygnathus barbarus – Nerophis ophidion
• Syngnathus hippocampus – Short-snouted seahorse

Pegasus (Seamoths)

• Pegasus volitans – Longtail seamoth