A mob of mutants on the attack.
The Mutants are a form of human derivation found throughout the Imperium of Man and in the wider galaxy beyond. Mutation often occurs as a result from exposure to many environmental factors, such as pollution, radiation, and limited exposure to the Warp. Though many mutants are born the way they are, mutation can occur later in life due to the corrupting influence from the Warp, such as where a planet may exist in a Warp anomaly, a psychic power gone awry, or actively worshiping Chaos.
Due to the random and chaotic nature of mutation, no two mutants are alike.
Mutants and the Imperium
In the doctrine of the theocratic Imperium, any deviation from the holy Human form is considered a sin to be punished with suppression, and even death. This gives rise to a rabid xenophobia, which extends to mutants. While this is held largely as an ideal, the pragmatism of the notion is one of the Imperium's bulwarks against Chaos; while many, perhaps even most cases of "benign" mutation on Imperial worlds occurs due to a polluted environment, removing any possible taint of Chaos may be the difference between communal survival or damnation.
As mutation is considered a crime and a heresy, it is punished on most worlds with death, leading to many mutants being killed on sight, and many mutant infants being abandoned to the elements or killed outright by their parents or the community. Any mutants who survive to adulthood are often pushed to the extreme fringes of society, such as living in the wilds or the abandoned lower levels of an arcology. As can be expected, most mutants develop into renegades, or gather in communities where they can live their lives away from the eyes of the world.
On some worlds mutation has a degree acceptance, and mutants are allowed to survive, albeit as second-class citizens as best. In the Realpolitik of the Imperium, some mutants can gather many followers and become quite powerful in their own right. Many mavericks in the Imperium, such as Radical Inquisitors or Rogue Traders will employ mutants, even treat them well, if their talents and faith are found to be sufficient.
An ancient strain developed in the Dark Age of Technology, Navigators are one of the most stable deviations of humanity in existence. Outwardly, Navigators, for the large part, can pass off as a baseline human with the exception of a third, "psychic' eye placed somewhere on their body, typically on the forehead. The third eye allows a Navigator to peer into the Warp; while this is typically used for navigating in the Warp literally by sight, it does possess other applications which may vary from case to case. But, invariably, making eye contact with a Navigator's psychic eye is a traumatic and fatal experience. Navigators will keep their third eye concealed for most of their lives, exposing it only in private to perform their duties.
Though the comprehensive genetic engineering and general stability of them, Navigators would probably be better classified as a human subspecies, but they are officially classified as mutants by the Imperium. Due to the general physical stability of their "mutation", and their psychic sight being the Imperium's only method of FTL navigation, Navigators are generally begrudgingly tolerated, though they have the position of power in most negotiations with Imperial institutions for rendering services. Any single Navigator house is often among one of the most wealthy and successful associations within the Imperium.
It should be noted that due to the nature of their talent, Navigators will develop minor, if unsettling mutations over the course of their lives, such as growing an extra joint on their digits, becoming incredibly tall and slim, or developing translucent skin. Senior navigators are often foreboding individuals who are clearly not quite human anymore.
Psykers
Psykers, while classified as a type of mutant, are another discreet strain of humanity almost entirely. Whereas mutants are seen as twisted by the power of the Warp, psykers use their mind to bend the power of the Warp to many fantastical effects. Psykers are rightly feared throughout the Imperium, not just for their supernatural power, but also due to the side-effects of using that power. As they are most often at risk for unmitigated exposure to the powers of the Warp, psykers are more prone to insanity and mutation than most of humanity, in addition to other possible catastrophic effects. As such, many unsanctioned psykers develop degrees of mutation over the course of their lives.
Mutation and Alien Species
Strangely, most aliens show little to no mutation, at least any that are visible to an outside perspective.
The Eldar, including the Dark Eldar and Exodite Eldar, shun Chaos after the fall of their empire. Craftworld Eldar and Exodite Eldar live tightly disciplined lives, leading to their psykers having nearly perfect control over their powers, giving them virtually no negative side-effects. Practition of psychic arts are one of the few things forbidden to the Dark Eldar, giving them virtually no concern towards mutation.
Orks are protected from the touch of the Warp, though the exact reason is unclear. Ork psykers also draw power from the WAAAGH!!, a gestalt psychic field produced by the Orks rather than directly from the Warp. In effect, this gives them a level of insulation from the most of the Warps ill effects, though many of these "weirdboyz" still develop eccentricities or degrees of insanity.
Tau are known to have a low psychic presence. In addition to having no psykers, they are particularly resistant to the Warp to the point that they are somewhat immune to some psychic abilities that interface directly with their mind (e.g. telepathy), though it doesn't mitigate abilities that work with physical forces (e.g. telekinesis, pyrokinesis). On top of their superior technology which consistently runs much more cleanly than any Imperial counterpart, or possibly due to the relatively new presence on any planet that hasn't been tainted by centuries of heavy industry, Tau have no worlds where the environment is a corrupting influence. There are no known Tau instances of mutation.
Not mutants per se, Tyranid Genestealers are known to hijack a creature's natural biological processes so that their offspring are bizarre hybrids of genestealer and the parent species, until they produce perfect "replicas" of the parent species as well as more purestrain genestealers. Like the Orks, other Tyranid creatures utilize psychic power gathered from gestalt psychic force, in this case in the form of focusing the power of the Tyranid hive mind. Tyranids are also genetically adaptable and rewritable by design, and evolve to adapt to a new environment or even a specific obstacle quite rapidly. The only known example where Tyranids have undergone involuntary, catastrophic mutation is the Ymgarl genestealers, where a brood of genestealers had experienced an unknown event on the moon Ymgarl, and now rapidly mutate from one variation to another in a matter of minutes. The Hivemind often goes out of its way to avoid reabsorbing the mysterious Ymgarl brood.
Mutants and Chaos
One of the easiest means of mutating is worship of the Ruinous Powers, deities who call the Warp home. While this usually entails rituals to thin or tear down the veil between warpspace and realspace leading to Warp exposure, a particularly favored disciple may be "gifted" a mutation as a reward as a mark of favor from one of these deities.
Some of the few safe havens for the forces of Chaos are within warpspace anomalies, due to these areas of space being unnavigable to the Imperium. As being in these places leads to at least a limited exposure to the Warp, cosmetic mutation may crop up on any given individual at any given time, and is a common occurrence; and in some places is seen as a mark of favor of the gods. Severe mutation is also not uncommon, and instances of born mutants occurs with much higher frequency than on any given Imperial world. Followers of the god Tzeentch, the god of change, are particularly prone to the most frequent and bizarre instances of spontaneous mutation.
Voluntary possession by a Daemon is considered an extreme act of devotion, and often reserved to those who are especially favored by a warlord, or those who have a particularly strong will or a special relationship to a daemon and can be trusted to keep the beast within under control during battle. Being host to a creature born from the substance of the Warp is particularly disastrous to the physical body, and rapid and dramatic mutation is invariably the result with life expectancy of these individuals is horribly brief. There are some, very rare instances where host and daemon are in an unusually stable synchronicity, with mutation receding when the daemon goes dormant, or the mutations have long term stability after the initial traumatic change.
Few of the followers of Chaos live long enough to see their corruption play out, but of the few that do most will see dire consequences. When one's body and soul is infused with too much of the Warp, both will collapse in mutation, the individual becoming a twisted, constantly mutating creature called a Chaos Spawn. Most spawn are bizarre creatures that can appear as anything from a puddle of screeching ichor to a writhing mass of eyestalks to hulking monstrosities covered in lashing tentacles and snapping, irregular mouths. While virtually every Chaos spawn is unique and has a horribly short lifespan, the largest and most dangerous will be kept alive and fielded as beasts of war. The only way to avoid this fate for those too engulfed with the power of Chaos is to hope to gain the attention of one of the gods, and be elevated to daemonhood. This fate is the ultimate hope for many champions of Chaos, seeking terrible power and immortal life as a demigod Daemon Prince, and such is the nature of Chaos that nearly all of them will fail.