The everyday concept of fishes tends to exclude more than a few. If scales, fins and gills were all required, catfishes, hagfishes and lungfishes wouldn't qualify.
Taxonomically speaking, there is no official classification called "fishes". Taxonomy is the science of classifying and naming living things.
Unique two-part names are assigned to each living and extinct species. The first part of the name is the genus and the second part is the specific epithet. For example, the scientific name for the Greenland Shark is Somniosus microcephalus and for the Pacific Sleeper Shark it is Somniosus pacificus. Like a last name shared by related family members, the genus name Somniosus is shared by related species. Other shared names above the level of genus are used to describe more inclusive groupings of related living things.
The basis of modern classification considers only lineage. Clues to this are found in physical similarities. Generations of research conducted by naturalists and scientists, particularly the study of fossils, shows that living things have become more varied with time. Rather than developing in a random way, plants and animals modify and build on what was there. New species are the result of incremental modification of inherited features over very long spans of time. Sorting out who-is-related-to-who in the previous generation is a complex and difficult task for someone who was not there to witness it. It's a little like having to describe fashion trends based on a pile of clothing collected over a few centuries. Recognizing significantly transformative events takes a little work.
Newer imaging techniques, embryological studies and molecular (DNA) analyses made possible by rapid technological advances have resulted in a flurry of adjustments to the family tree of fishes. Nevertheless the basic framework of the tree that predates the digital revolution is still remarkably accurate. And even with modern technologies, murky branches of the family tree of fishes remain for future scientists to tackle.
Ocean Sunfish or Common SunfishMola mola.The currently accepted scientific name for the Ocean Sunfish is the name given by Linnaeus in 1758, Mola mola. However the image above, from 1887, refers to this fish as Mola rotunda, as defined by Cuvier in 1798. Since ... rather than the names changing over time, it is the definition of the name that changes. All the names continue to have meaning even if one is accepted in usage today. To be clear, scientists refer not only to the two-part name of a species, but to the definition they use, e.g. "Mola mola, Cuvier, 1798. To learn more:• Exhibit: Source of image - "The Fisheries and Fisheries Industries of
the United States", NOAA. • Synonyms of Mola mola
Original literature contains terms and concepts that were current for their time. For example the term "Pisces" is no longer as an official taxonomic group. If you think of the categories of classification as file folders and the types of animals as papers that belong in particular folders, the filing system has changed. Not only have the names of the folders changed, but the rationale for the order of the categories and who should be in each folder have changed also.
Since it can be hard to keep up with all the name changes, we present the categories in a general way, so you can get a feel for how fishes are categorized today. For fish specialists, both the archaic (outdated) and new names are important to know in order to understand the meaning of historical documents regardless of when and where they were written. An older scientific observation written in another language using archaic terms does not invalidate a good observation.
What is the taxonomic category that contains all fishes? It is Craniata. The group name "Craniata" covers the section of the tree-of-life on Earth that begins with the earliest fishes. Those earliest fishes were ancestors of the modern hagfishes.
Craniata is a group name at the level of subphylum in the Linnean system. You may be familiar with the seven main levels of the Linnean system - kingdom, phylum,, class, order, family, genus and species. The nearly universal use of the prefixes "sub", "supra" and "infra" for each of the seven levels shows that forcing the categories of life into seven fixed steps is getting harder and harder to do.
However, not all craniates are fishes. Craniates also include the tetrapods or four-limbed animals with legs, arms, or wings that eventually populated land. The descendants of fishes that moved to land came from the branch of fishes that includes lungfishes.
Channel catfish Ictalurus punctatus. The Channel Catfish is soft to the touch because it has no scales, but does have sharp spines at the leading edge of the dorsal and pectoral fins. Although many local reservoirs, lakes, ponds and streams are stocked with this popular fish, it is native to the southeast and midwest U.S., and Canada.
Image courtesy Bureau of Reclamation, U.S. Department of Interior.
More about Channel Catfish:
• Animal Diversity Web • Map of native range
Fishes and all their subsequent descendants are all craniates because they inherited craniums consisting of skulls, brains and highly-developed sense organs around the head. The arrival of the first craniate on Earth marks the development of features that we consider central - the brain that eventually gives humans the capacity for language and culture, including music and art.
Features such as the gills and notocord which we associate with early fishes already existed in animals such as amphioxous (before the first fishsz and craniatez appeared).
Although they had skulls and brains, the earliest fishes did not have true bone, jaws or teeth made of more advanced materials such as dentin and enamel, or flexible scales. Once these useful and enduring characteristics developed over time,
they were passed down from one generation to the next over the last 530 million years.
What do we know about who is related to whom? Explore the larger diagram below to see where craniates fit into the tree of all life on Earth. Open the smaller diagram to explore how different groups of fishes are related to each other.
How craniates fit into the entire tree-of-life on Earth
Explore the rollovers and click on the one that flashes to move to the next level leading to craniates.
Note: We only show detail along the path to craniates.
Jeff Graham, marine biologist - The First Gasp of Air: The Incredible Story of Air-Breathing FishPerspectives on Ocean Science, Birch Aquarium at Scripps & UCSD TV
THE BIG PICTURE
If living things have adapted to change in the past, what makes human-induced change so problematic for many native species?
THE BIG PICTURE
The tree-of-life grows more branches forward in time. Your genealogical tree has more branches into the past than the future.
How are these two observations both possible at the same time?
WEBQUEST
The best preserved fossils show remarkable skeletal detail.
Find the most complete fossil fish skeleton (that is not a shark or ray).
Find the most complete fossil shark skeleton.
Was it easier to find examples fossilized skeletons of bony fish or sharks?
First modern classification of living things - the Linnean system, 1753. You may be familiar with ranks in this system - Kingdom, Phylum, Class, Order, Family, Genus and Species. • Linnaean taxonomy
How do we know who's-related-to-whom?    
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How do we know who is related to whom?
Similarities and differences between fishes provide the clues to relationships among species. Unlike relationships between living individuals of the same species, where reproduction and offspring might be observed, the evolution of differing species most often occurs too slowly to observe in a human lifetime.
Like family resemblance, similarities and differences help to identify relatives because traits like eye color or the posession of brains is inherited.
But, single traits aren't that diagnostic because many unrelated inviduals may share a trait such as hair color or fin type. Biologists consider multiple internal and external anatomical traits and less obvious clues that include the development of embryos and molecular structures within cells, like DNA. Both embryonic development and molecular structures are still inherited features of animals.
DNA is the equivalent of the entire digital file that instructs an organism how to build itself with particular traits. DNA itself is inherited so with the exceptions of copying errors, the more similarities, the greater likelihood two animals may be related. Like other characteristics, individual genes within DNA may be possessed by many species, but the coincident occurence of many genes indicates a close relationship. For many living things, where it fits withn the tree-of-life still remains to be determined.
Strucure of the DNA molecule.Every living thing inherits DNA from its predecessors. DNA is carried within the nucleus of each cell in every body. DNA tells your cells how to build themselves, tranmitting traits like eye color, and transmitting inherited characteristics such as predisposition to diseasep. Some characteristics are influenced by both genetics and environment.Image from U.S. National Library of Medicine.
Molecular clocks - how we know when ancestors separated
In addition to DNA in the nucleus, there is DNA outside the nucleus in structures called mitochondria. Mitochondrial DNA is called mtDNA for short.
Unlike DNA in the nucleus, mtDNA is inherited from just the mother, so it should not change from one generation to the next. Two species that had a common ancestor, like the common ancestor of both Thresher Sharks and the Great White Shark should have the same mtDNA.
But as time goes by, mtDNA changes as it is replicated into the cells of offspring, because copying errors (mutation) occur and accumulate over many generations. When those errors are not fatal, they are be passed onto subsequent offspring. The more time elapses, the differences in mtDNA between two speciesb become increasingly different. The degree of difference tells how much time has occurred since the sharing of a common ancestor or time of separation if you know how fast copying errors accumulate.
Dates are more certain when multiple lines of independent evidence point to the same date. Fossils provide an independent line of evidence. For example the age of a fossil ancestor to both Great White Sharks and Thesher Sharks can be compared with the time of separation based on DNA from living specimens. If the dates determined by two independent methods are consistent, it increases confidence in an estimated age of the branch of the tree-of-life.
Typical structure of an animal cell.Image from National Institute of General Medical Sciences.
How do you recognize a new species of fish?    
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How do you recognize a new species of fish?
American EelAnguilla rostrata.Forms at different lifestages can be so different that they are not recongizable as a single species. Appearance at different life stages - A) leptocephalus, B) glass eel, C) yellow eel and D) adult stage.Image courtesy More about American Eels:• Life cycle of the American Eel • Where Have all the Eels Gone?
Knowing a fish is like knowing someone, it involves being able to recognize them, and knowing their names and more personal details, like what they looked like when they were younger, their favorite foods, and how they make a living.
Recognizing a stranger in the neighborhood requires familiarity with everyone else who already lives there. Since there are so many different fishes on our planet, it takes expertise to recognize a new one. When a new fish is discovered, the discoverer gets to name the fish. The species part of the 2-part name is open, and sometimes the genus too, but the genus name and categories above it are defined by how that new fish fits into the tree-of-life.
The discoverer declares the new fish and its name by writing a scientific report that gets published in a peer-reviewed journal. Peer-review means that other experts in the field get to grill you on your conclusions before a publisher will print your article. The specimen or specimens on which the discovery and first description are based are sent to be archived in collections at museums, or research institutions like Scripps. Then they are available to others who want to identify their own specimens by comparing them with the original.
What is a species? Individuals that interbreed and produce fertile offspring belong to units called species. Because they are related by a common ancestor, individuals within a single species possess some similar traits. The species to which an individual belongs may be based on observation of anatomical, embryological or molecular characteristics of a living thing. The concept of species is both obvious and extremely complex at the same time.
While traits are important in identifying different species, it can be misleading to rely on just one because some traits appear in unrelated families. For example, many family members might have the same hair or eye color, but then so do many people outside the family. Rabbits and cats might have the same fur color, but clearly they are not of the same species.
So scientists consider multiple inherited traits to identify the species of an organism. The type specimens in a "comparative" collection at a museum are used in comparison for the purposes of species identification. On rare occasions, that work reveals that a species is new and previously undescribed.
David Starr Joran was a well-known icthyologist and president of two universities - Indiana and Stanford.
What fishes tell us about ourselves    
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Neil Shubin, fish paleontologist - Finding Your Inner FishUCSD TV
Craniates are the first animals with brains, skulls and jaws, key parts of ourselves. They are the ancestor to four-limbed land animals that include humans. Understanding the past helps us understand the way we are today.
Well known paleontologist Neil Shubin in referring to the anatomy of his head and the seemingly illogical construction of its wiring, the major nerves, are like an old building that's been renovated by modification-after-modification of old infrastructure. He says, "Nobody in his right mind would have designed a building from scratch this way."
Being a paleontologist. Neil Shubin thinks it enables him to teach anatomy to first year medical students in a way that makes more sense, because his understanding puts things in context.