Note: the events I'm about to outline are the current version as Blizzard presents it, which is considered to be the canonical version. If you remember differently from the RTS, that's because it was different then.
Untold thousands of years ago, Sargeras, the champion of the Titans, went mad. Confronted with the unfathomable evil of the Nathrezim, the corruption of the old gods, and chaos itself, he decided that the Titan's plan for order and creation in the cosmos was doomed to failure. Oblivion and chaos were not only the destined fate of the uncountable reaches of existence, they were all existence deserved. And so, Sargeras sought to undo the work of his fellows and destroy everything they sought to make. To do this, he needed a host as terrible and powerful as he himself was, and he found the seeds of this dread army on the world Argus, in the already magically gifted and potent eredar. So mighty were the eredar that they no longer feared death through natural causes or age, and the three mightiest and wisest of their people were Archimonde, Kil'jaeden and Velen, a triumverate among them. To this triumverate Sargeras appeared in all of his titanic majesty and offered them power and knowledge beyond that which they could possibly aspire, to walk the surface of countless worlds and see existence in a way none of their people ever had. It sounded perfect. It was perfect.
A perfect lie. Velen, suspicious of the offer, was given a vision of the future: his people corrupted striding the surface of world after world not as explorers, but as destroyers. Aided by the mysterious Naaru, Velen gathered what few of his people he could and fled the inescapable doom that awaited them if they remained on Argus. Enraged, his fellow triumvirs (especially Kil'jaeden, who had been as Velen's brother and who felt personally betrayed by him) stalked these exiles, or Draenei in the original eredar language, throughout the cosmos from world to world. The pattern always the same. Always the draenei would settle on a new world and for a time be at peace, always Kil'jaeden would find them, always the hunt would resume. It might have continued indefinitely, in fact, had the draenei and their naaru allies not crash-landed on a relatively pleasant but unremarkable world whose native inhabitants had not even bothered to give a name.
The draenei named it Draenor, a world meaning 'exile's refuge' and settled in. They found relatively little to conflict with their new neighbors, a race who called themselves orcs. For over five thousand years, the orcs and draenei coexisted, the draenei in their salvaged crystalline cities, the orcs in their nomadic, shamanistic society. They occasionally met but for the most part left each other be, the orcs finding the draenei strange and aloof, the draenei not wanting to interfere in the development of orc society. Then, as had happened before, one of Kil'jaeden's agents found them. But this time, Kil'Jaeden was almost more interested in the orcs than his old enemies. Here were a people perfectly balanced between savagery and restraint, raw fury and contemplation. Their grasp of shamanistic magic was unlike his own people, and yet presented opportunities, as clearly orcs had an aptitude for summoning and controlling entities that rivaled that of the eredar themselves. This, thought the master manipulator, this is a people I can make use of. The orcs had a potential that, for all their wisdom and power, the exiles hadn't understood. (Save perhaps Velen himself, when he met Durotan and Orgim Doomhammer.)
And so Kil'jaeden the Deceiver did exactly that, deceiving first Ner'zhul and through him, the orcs as a whole. Slowly at first, and then more quickly through Ner'zhul's more compliant apprentice Gul'dan, Kil'Jaeden taught demonic magics to the orcs, while also teaching them to use the aggressive nature they once employed in hunting and testing their strength against the elements to dominate and destroy the draenei instead. Not expecting attack from a quarter they'd so long been at peace with, the draenei fell, and were nearly destroyed by this unexpected threat which turned both numbers and new powers against them. (It didn't help that among the orcish numbers were Durotan and Orgrim Doomhammer, who'd been inside a draenei city and knew how to bypass its defenses). An attempt to broker peace at the site the draenei came to land, the sacred mountain Oshu'gun, only exacerbated the issue and ultimately led Ner'zhul to be replaced by his even more aggressive and power hungry apprentice, and Gul'dan prosecuted the war with the draenei with no regard to the truth of Kil'Jaeden's original accusations.
In order to make sure the war moved forward even as the orcish shamans began to lose their powers (the elemental and ancestral spirits abandoning them) Gul'dan moved quickly to teach warlock magic to the former shamans of the orc clans, especially his own Shadowmoon and those of the Blackrock clan offered to him by Blackhand the Destroyer, Gul'dan's chosen puppet and first Warchief of the Horde. This Horde was born out of orcish traditions from the long wars with ogres and gronn twisted to a new form, and eventually Blackhand even offered his own children (and those of others) to the Warlocks and their demonic, life draining magics, aging the children to adulthood so that they could fight sooner. The orc traditions of honor were turned inward, creating a society ripe for Gul'dan's last act of betrayal and destruction against his own people.
On the orders of Kil'jaeden, who wished to ensure orcish obedience, he called forth a demon, the dread Mannoroth. This pit fiend had once walked the surface of Azeroth during the events of the Sundering, and it was his blood that was poured forth into a great vessel, and it was Grom Hellscream of the Warsong Clan who first drank of it: indeed, all the various orc chieftains save for Durotan of the Frostwolves and his childhood friend and ally Orgrim Doomhammer (second of the Blackrock Clan and thus Blackhand's second in command) drank of the blood, and felt at first the enormous power and later the far more enormous cost of the power so gained. Fueled by this new demonic lust for battle, the last draenei cities were destroyed by the Horde, and their inhabitants driven into hiding in swamps and other desolate corners of the world. So triumphant, Gul'dan's Horde began consolidating under the secretive Shadow Council of the corrupted Temple of Karabor (now the Black Temple) and only the actions of a disgraced Ner'zhul helped preserve the Frostwolves as the last uncorrupted clan of orcs.
While this occurred, their ancestral home in Nagrand was turned into a quarantine zone when a mysterious disease known as the Red Pox struck many orcish children and other uncorrupted orcs. Unlike the Frostwolves who, despite not drinking the demon blood turned the same greenish color as those who had, those survivors of the Red Pox who were quarantined in Nagrand avoided that fate and are today the last remaining brown orcs in existence.
Meanwhile, Gul'dan had been seemingly abandoned by Kil'jaeden, who grew disenchanted with his blood crazed army now that they'd seemingly killed his ancient enemies. However, Sargeras himself had never forgotten his defeat on Azeroth and was in the process of taking steps to remedy it - he discovered that Kil'jaeden, his student, had either consciously or unconsciously done the same as he himself once had and corrupted a race with great potential to act as servants. Seeing more in Gul'dan's power lust than Kil'jaeden had, Sargeras reached across the Twisting Nether and led the Arch Warlock to construct the Dark Portal itself in order to breach the Nether and lead his Horde to Azeroth. Stranded on a slowly dying world where the spirits refused to answer and which only grew more sterile and desolate with each demon they summoned, the Horde was eager for a ripe, lush world to conquer. The Black Morass was brooding, forbidding, and teeming with dangerous life... but to a blood crazed orc, it didn't matter. A fetid swamp full of insects and reptiles and enormous arachnids seemed positively inviting compared to the lifeless wasteland of Hellfire, and the Horde eagerly poured forth into Azeroth.
Next week we'll take a look at both the Horde and Allaince through the First, Second and Third wars and how we got to the current state of affairs with a unified Alliance and new Horde.