If you were to look at the oceans 530 million years ago, you would be amazed by the wild array of creatures thriving in the waters. The seas abound with robust rainbows of corals and starfish. Huge schools of jellyfish pump through the waters while the sea floor is alive with a variety of mollusks and crustaceans. Life would likely have appeared to be as diverse as it could get. Then in the waters off the coast of China appeared a new, tiny little creature: Myllokunmingia fengjiaoa.
In the late-1990s, Chinese scientists found this 3-centimeter long little organism in the rocks of the Yunnan province. Although only one single example of this organism has ever been found, it has been identified by some as the start of a huge new branch on the tree of life: The vertebrates. It is proposed that from this small little creature – which is the first to have displayed a notochord and dorsal nerve cord – the entire array of vertebrate sprang: Fish and eventually reptiles (and birds), amphibians, and mammals.
So before you can understand how the world of fish came to be, you must start with these early ancestors. Vertebrates are members of the phylum Chordata. These chordates share three key characteristics in common:
Notochord: A flexible, longitudinal rod present in all vertebrate embryos and some adults. This device served as an early “backbone” for this family of creatures. 
Pharyngeal Slits/Clefts: These small pouches/openings in the body of the organism to allow the water taken in to exit the body. In fish, these are now called “gills.” Later in the evolutionary universe, these pouches would evolve into lungs for the land-living vertebrates.
Muscular, Post-Anal Tails: Although in some species, the post-anal tail is so small to be noticed, all chordates possess a tail that extends posterior to the anus.
The early chordates started as lancelets and tunicates. Lancelets are larger than their ancestor the Myllokunmingia – reaching a 5-centimeter long bladelike shape that allows them to dig into the sand and suspension-feed (feed off of suspended particles/organisms) for a lifetime. The tunicates (sea squirts) are less-genetically similar to the rest of the chordate family, sharing only 9 Hox genes instead of the standard 13 (both sets in a single-cluster), but they do display the key characteristic of the chordates during their larval stage. 
So how did these simple feeding machines evolve into the higher creature, fish? That is where the Craniates come in.
The Evolution of Fish: Craniates
Chordates had the “chord” or early backbone that allowed the body to take shape and the digestive tract to form from mouth-to-anus along the body. But they lacked one common characteristic of higher animals: A head. This “head” was developed through the formation of a brain at the anterior of the chord. This brain required protection and therefore evolution provided the early skulls – either bony or cartilaginous – to protect the brain, and eventually other delicate items such as the olfactory system and inner ear. 
On a genetic/scientific level, craniates possess two clusters of the discussed Hox genes, as opposed to the single-cluster of lancelets and tunicates). The development of the brain opened the door to a huge spectrum of evolutionary change. This genetic shift allowed for the creation of many critical variances in addition to the brain. These changes included the development of the neural crest, a collection of cells that form at the dorsal margin of the neural tube in the embryo, but later shift throughout the body to form such evolutionary leaps as teeth, skulls, and inner layers of the facial skin, as well as the eyes and other sensory organs. 
The transition from brainless chordate to craniate happened during the same period as many other evolutionary changes, generally known as the Cambrian...