Old Ones (Warhammer)
Old Ones of Warhammer Fantasy Battle and Warhammer 40,000 were major actors in the deep backstory of both worlds. There is some debate about whether they are actually the same people in each, and these theories are explored in the Warhammer Meta-Setting article.
Warhammer Fantasy
In Warhammer Fantasy Battle, the Old Ones are psychic frog-men from beyond the stars (big silver space-ships are mentioned even in the latest main rulebooks). Knowing Chaos would one day appear in this reality and attempt to consume it (how they knew is unspecified) they decided to create a race of beings capable of keeping Chaos at bay forever, or even beat them (we don't know how ambitious they were). They reshaped the world, during which they created the Lizardmen races to aid them. The Slann were simply less intelligent reproductions of themselves, the Saurus were their bodyguards and had very few thoughts in their head other than whatever their current task is and the general calm reverence of the Slann and Old Ones (so born Space Marines), and the Skinks as the tiny frantic servants to the Slann. Requiring more magical power, they established Realm Gates at the north and south poles of the world, through which they were able to travel freely between the world and wherever they came from. They also siphoned pure (AKA formless raw potential, pre-Chaos God alignment) Chaos magic into the world in order to protect the world from Chaos, which worked exactly as well as you'd imagine. They made peace with the local natural intelligent life, the dragons, and educated them as best they could. This knowledge would later pass onto the first created race of the Old Ones as the two races would become BFFs. Old Ones noticed the presence of greenskins around this time, the Old Ones brought to the world unknowingly in the form of spores which grew up to be the greenskins. They tasked the slow-reproducing Lizardmen with wiping them out, again with predictable results.
First, they created Elves. They shaped a continent called Ulthuan which actually floats above the ocean like a giant ship for them to dwell on, and instructed the Slann to teach the earliest of them magic (it's unknown if the Elven gods were formed by the Slann or Old Ones, or if they came later out of belief; evidence supports the former as Isha is the mother of all mortal elves with Kurnous and as such the gods may have been proto-elves). As they surveyed the Elven race, they decided the Elves could not beat Chaos alone due to being frail and having a low birth rate despite potential for mastery of magic and a VERY strong resistance to the Warp.
Next, Dwarfs were created. The Dwarfs actually resisted magic innately and in their presence it shifts back into formless current and seeps back into the Warp. The Dwarfs were hardy, and could physically bully magic into doing what they wanted it to (hence becoming great smiths of magic weapons free from Chaos taint using runes). However, the Dwarfs were stubborn and would not adapt fast enough in the face of demon trickery. The Old Ones abandoned yet another of their creations.
The next race created was humanity (in the heart of Africa in the fertile crescent, which wraps around the South Eastern shore of the Mediterranean Sea and a little inland at Syria and Iraq), which combined the magical aptitude of the elves (to a lesser degree) with the durability of the dwarves (to a lesser degree). Humanity's short lifespan with rapid reproduction along with ambition and lust not seen in their elder races combined would enable humans to have time to adapt and overcome anything Chaos could send at them. But humanity was too malleable. While the great ambition and adaptability could be a great strength against Chaos, it also made them more susceptible to the influence of Chaos than elves or dwarfs (as proven later when humans - including Beastmen - make up the majority of Chaos' forces).
The Old Ones created Halflings next, although nobody really knows why. They were resistant to mutation but that's about it. Small, frail, cowardly and unassuming, they were an abysmal failure as Halflings aren't really good at much other than cooking and eating. In a way they were the proto-Ogres.
Various other races were created, more or less filling the gap of both anything added to the game down the road as well as anything fans can come up with. The sky titans were one such race, having the magical aptitude and intelligence of Elves, and the durability of the Dwarfs. However, they were too isolated and too solitary, and were likely just an artistic project. There may have been others, but it is likely that many of these proto-races were wiped out by the Lizardmen or if too much of a failure by the Old Ones themselves, with only the most "stable" being allowed to exist (men, elves, dwarfs).
Finally, the Ogres were created by combining the best aspects of Man, Elf, Dwarf and Halfling. They were highly resistant to Chaos yet still possessing magical talent, having a long lifespan like elves, with a fast reproduction rate they'd be able to outlast Chaos, being highly durable, being able to cooperate with just about any race and quickly adapt to their customs, and finally stubborn enough to not fall to Chaos willingly in most cases. In addition to this, they are able to survive on just about any food, from meat to tree trunks to rocks. Their only drawback was their enormous appetites. As the Old Ones prepared to educate their newest masterpieces, endow them with gifts and try to fix that kink, the Warp Gates collapsed and Chaos entered the world. The Ogres, left with a growing population in a relatively stable environment, were not gifted with any taught culture. As a result, despite being fairly intelligent creatures on par with dwarves, elves or humans, the ogres were not unified, and had to grow as a natural race, unaware of and unwilling to engage in the purpose they were designed for. They thus became tribes of increasing size which spread out across the world and served every faction (including Chaos and its servants) as mercenaries.
Why the Old Ones never looked at their failed creations and thought about putting them together in a lizardmen-style caste system is unknown. Dwarfs as the industrialists, artillery and infantry, Elves as artisans, scholars, cavalry, archers and mages, Ogres as the shock troops and heavy lifters, halflings as cooks, and humans to fill in anywhere they were needed and provide individual great heroes would have worked out perfectly.
Instead, Chaos ran amok as the Four and their allies got off their collective asses, gained followers and physical influence in the world, and started fucking shit up. It's worth noting there's a subtle disconnect from 40K in that Chaos and the Old Ones were there all along, as Fantasy Chaos has no Genesis true, kinda, but there's less metaphysical difference between the two settings than at first glance because, you know, warpfuckery; different worlds, same warp, so a few of the rules are different (what rules? It's the fucking warp), same Gods, too. As for the "emergence of the Gods" in 40K, they do coalesce psychically but also aren't bound by the rules of time (cf. the 40K Old Ones were against Chaos way before any of them were said to be "born"; and though Slaanesh is the edgy youngster "born" fairly recently it has been stated canonically to have influenced events before the Fall of the Eldar in 40K; it's probably the same for the others--imagine the time Tzeentch is having.) The exact nature of the Old Ones, the gods, and how the world got to where it is now is a subject of endless debate and conjecture among fans.
It's unknown what happened to the Old Ones. It's possible that they fell into the Warp and were consumed. It's possible they fled the world, leaving it to its fate as they tried again elsewhere. It's also possible they remain in hiding, either guiding the mortal races to grow in strength and thwart Chaos or watching as their master plan unfolds leading to true victory. Either way, they're gone.
Lizardmen began worshiping the Old Ones as gods, with Slann pondering the messages left by their masters on golden tablets (which is apparently how all Old One communications were relayed, just like the Mormons) to the smallest detail, and acted on interpretation. At times this has resulted in counter-productive things like an attempt at world recreation which caused most of the Dwarf race to die and greenskins take over their fortresses and breed in numbers never before seen. At other times great things have happened according to plan, such as when they have prepared for and beheld the coming of a god prophesied by the Old Ones, who immediately consumed the minions of a rogue Greater Daemon/minor Chaos God and drove him from the material plane.
At some point, one of the resident non-Chaos villains learned the words the Old Ones used to shape the world. With it (at GREAT physical and spiritual taxation of himself) he reduced fortresses the size of modern cities into atoms.
In older canon, the Old Ones did not create or predate the other races (in fact, one old lich mentions remembering the coming of the Old Ones with disdain as something that came long after his first death). Instead they were simply space travelers, and the Slann were their retarded and decadent inbred descendants.
The end times revealed that this warhammer world was not the first, but just one in an eternal cycle. While men, elves and dwarfs all seem to fit in with this cycle, the old ones do not. It has been suggested that the Old ones were actually the surviving slann from the last world, and that the slann who managed to escape the destruction of the warhammer world will return to the next one as the new old ones.
Warhammer Age of Sigmar
Now it is currently unknown who reshaped the world, but if what was told above is true, then the old slanns became the new Old Ones, deciding to reshape the world as 8 different realms made out of the Old World's winds of Magic, though all of the above has not been confirmed yet, what we do know is that the old ones did create the realmgates, portal to and from different realms, allowing connection and travel to other worlds , and presumably also created the allpoints, a mini-realm that acts as as a hub-world to access all other realms, which is right now in Archaon's possession... oops.
Also this would mean that technically, Lord Kroak is an Old One now, which makes sense given how stupid powerful he is.
Warhammer 40,000
In Warhammer 40,000, the Old Ones were a race or group of races that were among the very first intelligent races in the galaxy, if not the first (heavily implied to be so.) Usually, they are referred to as a single, specific race. However, Codex: Eldar 4th Edition, as well as some of the Deathwatch supplements, claim that they were actually a group of the earliest races, who all worked together, which, given that Chaos (such as it was back then) was anathema to him, makes us think of another "rainbow coalition" many millions of years later.
They were incredibly potent psykers (especially since the Warp was calm back in those days), had access to the Webway (if they didn't build it themselves, they certainly discovered and expanded it), and had supremely advanced genetic engineering techniques. They created the Krork (prehistoric Orks, in the same way dinosaurs are prehistoric birds), Laer, Jokaero (showing that they have a sense of humor), the Hrud, the Rashan, the K'nib, and many others; some of these were created solely as warrior-races, whereas many (like the human predecessors who didn’t exist then and so probably weren’t and some say beings that would evolve humanity’s ancestors were not altered or created by the Old Ones but instead left alone)(I had a stroke reading this) were created merely as part of planetary ecosystems, or maybe just for shits and giggles. They also “uplifted” ( in that they already existed but we’re still relatively primitive so the old ones made them smarter and probably gave them fire .) Eldar, and Necrontyr (but since the Necrontyr met the Old Ones for the first time much later, this claim is unlikely). Because they believe that they could one day achieve the same greatness they did… Good God how they were wrong (ironically a lost cause like the poor frail humans are destined to become New Man like the Emperor, far beyond mere Old Ones seeing as his blows during the duel with Horus could have destroyed planets according to the story), (More on that later). The Old Ones were immortal (due to evolving so damn hard that they became energy beings), a gift they seem to have given in some form to only some of their creations; and also, and of great importance, these races had souls, which gave them presence in the Warp, where the Old Ones were getting up to their own stuff in as well. This eventually of course lead to the warp becoming the fucked up place it is "today," but all because of a lot of drama with the lesser races. The Old Ones didn't intend (or did they?) for it to get that way because, being a race of Energy beings (at this point), it was more or less their home for all intents and purposes.
The Eldar in particular were one of the first races the old ones uplifted (or created, fluff varies), and due to their absurd reproductive capabilities (basically space rabbits) Were both technologically on par with the old ones, and the most populous race in the galaxy after only a few centuries.
It's basically impossible to talk what went down next without talking about what happened with the Necrontyr. The Necrontyr had grown up beneath a wretched sun that poured radiation upon them (this radiation may in fact have been Star Vampire shit or merely attracted them, more on them in a bit), so their lives were, without exception, incredibly short (although it's not clear how short). Nevertheless, they managed to scrape together a small interstellar empire, with different star systems ruled by different dynasties. However, with the First War of Secession, the empire fell into infighting, as the dynasties violently jockeyed for power.
The Triarch decided a war was just what the doctor ordered to keep the Necrontyr together, and so declared war on the Old Ones, claiming the casus belli of "you didn't share immortality with us poor, pitiful, mortal creatures." Though lore also says they just wanted medical help so they wouldn’t be in constant pain. The Old Ones refused. This was, as would be expected, a popular cause, and started the so-called War in Heaven. Why some races were gifted with immortality and others not is unclear, but is probably down to what their particular purpose was (one tenuous but curious connection between the Old Ones and the Cabal alluded to above is that the Cabal can apparently create Perpetuals. If there is a connection, and there are some other hints as well, then the Cabal is the Old Ones, or some vestige of a coalition of immortals appointed by them, trying to unfuck the fuckery that they fucked up the fucking warp with by screwing over the only being Chaos is genuinely so scared shitless of they cannot even say his mere title without agony and so just call him “The Anathema”.)
Anyhow, back to the War in Heaven. Despite having much greater numbers and mastery of conventional technology which matched or even exceeded that held by the Old Ones, the Necrontyr did not have access to the Webway, and so were constantly outmaneuvered (even though they could teleport across interstellar distances and build portals...so just suspend your disbelief at the out-maneuvering bit). Soon, the Necrontyr were scattered and left with only a few coreworlds to the galactic north. With the War in Heaven collapsing, the Second War of Secession began, and the Necrontyr began to tear themselves apart again.
Before Necrontyr society collapsed entirely, however, the Necrontyr discovered the C'tan, the Star Gods, leaching on some of their stars. The Necrontyr made metallic bodies for the C'tan, which barely contained their incredible power, as they were basically material universe's equivalent to the Chaos Gods.
The C'tan known as the Messenger (later the Deceiver) offered the Necrontyr a solution: living metal bodies that were nearly indestructible, in exchange for their service to the C'tan. The Necrontyr accepted, only for them to realize too late that their new bodies required the destruction of their souls and their enslavement to the C'tan. For some reason, the Necrontyr were also renamed the Necrons at this point. One of the C'tan, known as the "Burning One," also helped the newly-robotic Necrons enter the Webway using the Dolmen Gates. With the field leveled, the Necrons were now able to take the fight to the Old Ones.
At this point, the Old Ones created many of the aforementioned warrior races, especially the Krork, but even these couldn't stop the Necrons. The wild misuse of the Warp had also spawned the Enslavers (or, at least, let them enter the material universe), obliterating many of the Old Ones. The birth of Chaos caused by the corruption of the Warp by the dying emanations of countless warrior races probably didn't help either, to say the least. Incidentally, this also means that the current state of Grimdark in the galaxy is all their fault. With the Old Ones thus weakened, the Necrons and their C'tan allies were able to annihilate the rest of them, at least according to Codex: Necrons 5th Edition. After that, the eldar discovered that by using the webway could create constructs capable of housing the dead, and damage the C’tan. the Necrons exploited the weakened state of the C'tan and turned on their masters; while they were successful in breaking them into countless "shards" of their former power and permanently killed at least one, they feared the retaliation of the Eldar and the other surviving warrior races and went into hibernation until they were ready to rebuild their empire. Ironically they might have been able to play things off as them having been enslaved and blame the war on the C’tan. Especially after they shattered the C’tan.
Although most races aren't aware of their Old Ones heritage, they still made a great impact on the nascent races. In particular, at least according to Xenology, many races, including the Eldar, have very similar gods, including a bloody-handed warrior, a great smith, a life-giving goddess of the harvest, a laughing god, etc. It seems that these gods were inspired by the Old Ones, although whether they're based on particular Old Ones or just general concepts of what they did is uncertain. It was mostly conceptual though since the eldar and old ones were contemporaries by this point. If you read the examples of gods above and thought by yourself: "Haven't I heard of this in real ancient religions at some point?", and if you can then connect that revelation to The Emperor, congratulations - you know basic mythology.
Also, in Hrud mythology (again, according to Xenology), there's one last Old One named Qah that only left 500,000 years ago (i.e., long after the Necrons entered hibernation), promising to return when the Hrud reunite to fight the C'tan again. This would imply that, in fact, the Old Ones were not destroyed entirely by the Necrons, and a few hid or escaped. While this was presumed retconned for a long time, recent fluff has noted that Eldrad has predicted the impending return of the "Old Masters" and the newly discovered seventh Blackstone Fortress's pristine state suggests they may indeed still live. You can proceed with theorycrafting over whether they made a deal with the Emperor and/or some of the Eldar to fix shit up.
The idea that some of the Old Ones survived is also found in Grot folk tales. So goes the story, the last of the "Brain Boyz" (Ork term for the Old Ones) hid among the Krorks in the last years of the War in Heaven. But slowly, the Old Ones devolved into the servants of their former slaves. And being enslaved made them degrade further and further, until today they exist only as the Snotlings, those extra tiny Grots that can just about hold a box of tools without forgetting to breathe and keeling over. The Orks have heard of these folk tales, and get a good chuckle out of it; the story could be completely true for all they care, which is not at all.
Connections
In very early editions of Warhammer Fantasy Battle and Warhammer 40,000 (i.e. when the former was still called "Warhammer" because it was the only Warhammer, and when the latter was still called Rogue Trader), it was implied that the two universes were very closely linked, if not one and the same. Now, not so much; but the warpish links discussed above, while obscure and speculative, are probably still true. Chaos warbands in Fantasy could get their hands on bolters and powered armor, and Beastmen and Space Dwarfs (called Squats) were regular parts of Imperial and Chaos armies in 40K. The Old Ones were described as coming from space even in the 8th edition Fantasy rulebook, and the 3rd edition Necron codex suggested using Lizardmen minifigures to represent their descendants.