Yes, once upon a time, Beastmen were playable in Warhammer 40,000. And then they disappeared. But now they have reappeared, with a mention in the core rulebook and a presence in the Heretics & Renegades army list printed by Forge World!
Back in 2nd edition, Beastmen and other mutants were the byproduct of Genestealer Cults, which were a specific type of Genestealer infiltration, formerly called a Genestealer Clan, that started worshiping Chaos and the Ruinous Powers, thus becoming a Genestealer CULT. The army allowed for use of Genestealers, Beastmen, mutants and Demons. Later, the term Genestealer Cult was used for a general Genestealer infection, and the beastmen were shuffled off to the side in favour of a Genestealer Cult list having nothing to do with them, but that's fine as they then turned up in a playable mini-army in the Witch Hunters rulebook as an example of what the Witch Hunters fight against (called mutants in this case), and they also showed up again in the Eye of Terror codex, in the Witch Hunters case it's because mutations like that happen naturally in 40K, they're just usually killed when they're born and the army in question didn't follow the Imperium's teachings, and in the second case it was directly due to Chaos making a lot of mutants.
Now, they exist mainly in the fluff as a barely-tolerated strain of abhuman whose main use in the Imperial Guard is to act as meatshields so they can atone for being mutants. Some things never change.
In terms of temperaments and looks, Beastmen look and behave....exactly like their fantasy counterparts except instead or primarily worshiping Chaos they also worship the Emprah. Beastmen out of all the abhumans are one of the most variable and unstable, only avoiding the term mutants because they all kept a consistency of looking like goats, minotaurs, satyrs or any form of bipedal ungulates. Of course as mentioned, they are in a hairs-width of being completely labeled as mutants now because of how inhuman they look and behave. Seriously they possess a reputation for crudity, aggression and bad discipline and trying to lecture one is like trying to lecture a stubborn donkey. Back in 30k, the Imperium was much more forgiving to the Beastmen as they were often recruited into the ranks of the Imperial Army as part of the massive galactic expansion of the burgeoning Imperium of Man during the Great Crusade. Beastmen in the Imperial Army were regarded as useful if highly undisciplined warriors, and were ideal for suicidal assaults where brawn rather than tactical intellect was required. Other Imperial troops disliked them intently as they were quite rowdy, unsanitary and generally unpleasant for baseline humans to deal with.
Due to the wide variations of Beastmen, there are several breeds and sub-breeds that has popped out of the Imperium (AKA if you're familiar with Beastmen in Fantasy or is a Beastmen player, than you would be familiar with all of these). These are:
Gors: The most common type of Beastmen are called Gors, who can be readily distinguished from more lowly breeds by their horns. The number of horns is not important, although it is preferable that they should be on the creature's head. Gors take great pride in their horns and often polish, paint or decorate them to enhance their natural lustre or shape. Lowly breeds look to the Gors for guidance and leadership, praising them endlessly in victory, and grumbling behind their backs when things are not going so well. Most Beastmen battle-leaders and the top warriors will be Gors. Gors are further divided into two main sub-breeds and a less common third sub-breed. The two main types are the goat-horned Caprigors and the bull-horned Bovigors. The third variety is known as the Ungor, a Beastmen phrase which means something akin to, "not quite right Gors" or "no-horns".
- Caprigors: The most common type of Gor. They have curling or straight horns on their head like a goat or sheep. A Caprigor may have the entire head of a goat and often has goat's legs as well. A Beastman with these mutations but no others is called a Truegor. This title is also shared by some other kinds of Gor. A Caprigor Truegor is said to be bigger, braver and even more clever than other Caprigors.
- Bovigors: Not quite as numerous as Caprigors, a Bovigor bears cattle horns on his head and may have the entire head of a bull or an ox (Turning them into mini-Minotaurs). If he has a bull's head and either human or goat legs he is a Truegor. Bovigors are very competitive and like to think they are superior to other Gors. Most Bovigors believe that brawn is better than brains, and many possess a great deal of the former and very little of the latter.
- Ungors: Ungors are not as strong or robust of frame as the Gors, but they more than make up for it in sheer malevolence. They are physically smaller than other Beastmen and their horns, if they have any at all, are less impressive and less numerous. While Gors may have long and spectacular horns as deadly as any sword, Ungors usually have short prongs or horn buds sprouting from their skulls, not recognisable as those of a goat or any other type acknowledged by the Gors. As a result they are not considered to be "proper" Beastmen by other Gors. They look the most like Humans out of all the Beastmen (Saved for Turnskins).
Brays: The majority of Beastmen who are not Gors are called Bray. The name refers to the braying, whinnying, whooping cacophony that Beastmen make when they band together to fight or feast. Apart from lacking horns, there is very little consistency in appearance that distinguishes a Bray from a Gor. A very brave, cunning, and unusually lucky Bray can rise to become a leader, but this is not very common. Gors do not like Brays giving them orders, and a Bray who fails to show a Gor the proper respect is asking for trouble.
Turnskins: A Turnskin is a Beastman who was born human. The continual rate of mutation amongst the human population throughout the galaxy often results in hideous mutations. Human mutants are not tolerated in their own societies, and most of them are killed when their mutations manifest themselves, or are driven from their homes to die lonely deaths. The toughest and most cunning manage to survive their physical and psychological rejection and come to join up with bands of Beastmen. Regardless of their physical appearance, a Turnskin is always a Turnskin rather than a "pure" Beastman, which means he is the lowest of the low as far as the Beastmen are concerned. If a Turnskin has horns, they are sawed off before he can be accepted by other Beastmen, otherwise he could be mistaken for a Gor. AKA these guys get the worst short end of the stick.
Shamans: Shamans are a very special kind of Beastmen because they possess psychic powers. However, this fact alone is only a part of what makes them special. Shamans are the intermediaries between the Beastmen and the Realm of Chaos itself. They can spirit-walk in the Empyrean and talk with the very daemons of the Chaos Gods. Shamans never lead other Beastmen, but the Beastmen's strongest leaders rely on them for all kinds of advice as well as sorcerous aid in battle.
Minotaurs: As their name would give you any hints, Minotaurs are an unusually large and aggressive strain of giant Beastman, Minotaurs are comparable in physical size and strength to an Ogryn. These creatures are massive, bull-headed monstrosities that constantly hunger for hot blood and red meat. Often growing to twice the height of a man and far greater in muscular bulk, their thick-skulled heads are broad and ugly, and their horns can eviscerate with a single thrust. Minotaurs are possessed of a terrible hunger for flesh, particularly the flesh of Mankind. Yet it is not the gnawing hunger a mortal feels when deprived of sustenance, but a deep thirst for the unholy exhilaration the Minotaurs experience when they consume the flesh of their enemies. Of all the Beastmen, they are the most likely to join Khorne.
Of course now with the idiots running the Inquisition, the Beastmen are now viewed with scorn due to looking like an aborted lovechild of some intense furry-on-furry-on-space wolf yiffing. Consequently enough, it has led some Beastmen to start worshiping Chaos. Gee, how counterproductive eh?
Although, there are several signs that the Inquisition are not entirely wrong in their assessment. Besides the fact that Beastmen that turn to Chaos take to it like a fish to water, the extreme variation of Beastmen, combined with their tendency to start spontaneously appearing on Chaos-held worlds (the Tzaangors of the Planet of Sorcerers are heavily implied to be descended from what was left of Prospero's human population) indicates that Beastmen in general are indeed a breed originating from Chaos, just not in thrall to it by nature.
Thanks to the raging retards in the Imperium who just want to further dig a deeper hole in their own graves. Some Beastmen, fed up of being chased out by the wider Imperium decides to go all edgy and rebellious like a teenage kid in his mom's basement by joining the four ruinous powers. In certain cases, as with the Planet of the Sorcerers, the native population of a planet may mutate into Beastmen when it becomes a daemon world. These Chaos Beastmen are:
Khorngors, Beastmen of Khorne
Those Beastmen who serve the Blood God Khorne are known as Khorngors. The signature of Khorne is writ clearly upon the form of the Blood God's Beastmen. They have canine heads or faces, fierce snapping jaws, and teeth which drip with rank saliva. Their skin or fur is usually red and their eyes are all white with red pupils. Khorngor Champions often have fur which is especially impressive, either bright red, black with red flecks, or a strange metallic brassy colour. If the Beastmen has horns these may be twisted into the shape of the skull-like rune known as the Mark of Khorne. The same rune is often painted or burned onto their skin or fur, and can be tattooed onto their exposed foreheads. Beastmen of Khorne always fight in their own units, although they can be led by a Beastmen Champion so long as he does not follow any other Chaos God. Beastmen of Khorne hate enemies who are mortal followers of Slaanesh, including Beastmen who follow that patron. They also hate all enemy Chaos Sorcerers. They do not hate enemy Shamans who also follow Khorne, as they cannot cast sorcerous spells but have the power to nullify psychic abilities. Their hatred only applies to enemy troops, never to allies, even if they are followers of another Ruinous Power.
Pestigors, Beastmen of Nurgle
The Pestigors, the Beastmen of Nurgle, have blistered and broken skins, often red with cracked flesh and sores which have been given to them by a generous master. Their fur is matted and coarse, and their bodies are riddled with all kinds of disease. Yet they retain the morbid vigour that characterises their master so their afflictions in no way mar their battle-worthiness. The Mark of Nurgle is carved into their armour, daubed upon their clothes, and sometimes etched onto their skin by the path of disfiguring disease. Many Beastmen of Nurgle carry Nurgle's Rot, although thanks to their loyalty to Grandfather Nurgle, that terrible arcane disease will not affect them.
Slaangors, Beastmen of Slaanesh
Beastmen of the Chaos God Slaanesh, known as Slaangors, have white or near white fur and pale or pastel skins. Their eyes are green and are sometimes saucer-like in a similar way to those of the Daemonettes. The Mark of Slaanesh appears somewhere on them, painted onto their hides or carved into their armour, a bracelet or neck collar. Many of Slaanesh's Beastmen have the head or horns of a bull (known as Bovigors) just like the Greater Daemon of their patron god. And they all have huge dongers.
Tzaangors, Beastmen of Tzeentch
True to the Changer of the Ways, Beastmen of Tzeentch, known as Tzaangors, are spectacularly variable. They always have at least one outstanding feature, either brightly coloured or exotically patterned fur, or very impressively coloured or shaped horns. Their mouths are also more beaklike than goatlike, as befitting their association with Tzeentch. Other mutations are commonplace amongst Tzaangors. Where other Beastmen often have no mutations (beyond their already altered phenotype), Beastmen of Tzeentch always have at least one. Tzaangors so far are the only known breed of Beastmen that can also fight in a Chaos Space Marine army (specifically, the Thousand Sons), and not just in the Lost and the Damned. It is unknown if this is exclusive to Tzaangors from Sortiarius, but Tzaangors tend to be more intelligent and disciplined than other breeds, making them useful auxiliaries to a legion that is composed mostly of mummies and sorcerers.
Currently the only 40k Beastmen with models and rules.
After the momentous shift to 3rd edition, the idiosyncratic or sillier armies were largely removed from the game, so things like Zoats, Squats and Genestealer Cults would disappear. For their part, Beastmen have had a varied history on the tabletop battlefield, popping in and out of the editions at the whimsy of the upper management. Within Chapter Approved, Imperial Guard could take Homo Sapiens Variatus, by paying 30 points to upgrade a Conscript squad. Boosting their WS to three and granting them Furious Charge. Later, under Eye of Terror and Siege of Vraks part 1, though not referenced directly, you could make units of Mutants and call them Beastmen. It was only really when Imperial Armour Volume 6: Siege of Vraks part 2 came along that Beastmen really came back to the game as we know it in an "official" manner: Bloodgor Beastmen Packs could be taken by a renegades army aligned to Khorne, costing 6 points for a WS3, T4 Conscript equivalent with Furious Charge, two close combat weapons and the ability to rally when below half strength. Lasguns, Pistols or Grenades had to be bought for extra.
...Then they disappeared again, and didn't resurface directly. Until recently, but more on that in a bit.
Imperial Armour 13 and the collected reprint of Siege of Vraks both give current 7e rules for Mutant Rabbles, who are genuine Conscript equivalents who have a 33% chance of being horned/clawed, the rest of the time they are either ugly, smelly mofos or of the overly heightened senses variety, making it difficult to model them appropriately unless you speak nicely to your opponent beforehand. The beauty of the Mutant Rabble is the ability to buy a covenant of chaos for the squad champion, aligning them to whichever got you choose, and granting you the ability to distinguish between Tzaangors and Slaangors and so on.
Beyond 40k, if you look to the Imperial Militia and Warp Cults list for 30k, you do not just merely have the ability to field one single type of unit of Beastmen, but an entire army of them, manning your artillery or driving your tanks and are not automatically associated with traitors or the forces of chaos. By taking the right Provenances in your army you can have a whole army of T4 Abhumans Helots and call them "Variatus" or straight up take Fear causing, Feel No Pain, Rending mutants and call them "Beastmen", or mix and match Provenances to suit Your Dudes.
Then along came Warzone Fenris and Wrath of Magnus. While this gave the Thousand Sons a much-needed facelift, it also came with an unexpected update; Tzaangors now not only had models, but fight alongside the Thousand Sons! Could this mean more Beastmen models are on the way? The Emperor (and by Emperor we mean Sigmar, since the tzaangors are AoS sprues with chainswords/pistols thrown in as an afterthought) only knows...