The arrival of the Draenei shook things up on Azeroth. Natural enemies of the orcs, they quickly took up with the Alliance (after some brief "OMG are you demons?" confusion) and swore a vendetta against the blood elves. The blood elves, ostracized from the Alliance because of their comrades' activities on Draenor, decided it might be a good idea to join the Horde before the blue-skinned weirdos and their hippie cousins staged an armed intervention. The blood elves were viewed with suspicion by the trolls, orcs and tauren, but were rapidly embraced by the Forsaken and their formerly high elf queen. Working hard to rejoin their prince in Outland, the blood elves were unaware of the depths to which Kael'thas had sunk ...
While everyone was distracted by these new and exciting developments, the Burning Legion was making its own play for power. The demon lord Kazzak, realizing that his loot was horribly outdated, went in search of a way to open the Dark Portal and go into Outland to meet up with his friends. He found an "artifact of incredible power" that let him do so. Hmmm ... looking at Kazzak's new loot table, I see nothing of incredible power. He should drop something that lets you teleport between Outland and Azeroth.
In typical Burning Legion fashion, instead of, y'know, quietly slipping through and amassing a huge army on the other side of the portal and invading in the middle of the night, Kazzak sent a messenger to pretty much go from city to city and yell "HA HA, WE OPENED THE DARK PORTAL! COME AND STOP US! WONDERFUL GEAR AND REFRESHMENTS AVAILABLE UPON REQUEST! ONLY $50 AT BEST BUY!" Demons also poured out of the portal for ... a week or so, after which they apparently got bored and stopped invading Azeroth.
Millions of adventurers took up the challenge and headed for the Blasted Lands, where they were met by a mighty force of millions of adventurers from the opposite faction trying to complete the entering quests. But eventually, the armies of the Horde and Alliance stepped through the Portal and onto the Stair of Destiny, where they were able to pick up a quest and maybe buy some water before getting disconnected five times in a row.
Three days later, when the servers were stable, the adventurers began to explore this new world. A few things quickly became clear:
The Burning Legion had a stronghold and some teleporters around the area, but they weren't really doing a great job of invading Outland.
The discovery of a lost tribe of orcs and the remainder of the Broken draenei meant that both the Horde and Alliance had vital interests in the area, and were planning on
exploiting exploring it for all it was worth.
The refugee city of Shattrath, built by the Naaru and forbidding any fighting, guaranteed that we were going to end up running errands for a billion different warring races that no one would otherwise care about (i.e. arakkoa.)
While exploring the new areas, it became obvious that most of the problems in Outland were being caused by the terrible trio of Illidan, Vashj and Kael'thas. Vashj was draining all the lakes in Zangarmarsh into a giant reservoir in order to control the area politically (and maybe make a new Well of Eternity.) She was easily taken down by twenty-five adventurers, and Zangarmarsh was restored back to its ... lovely ... natural state. I'm sure the Marshfang Rippers appreciated it.
Illidan was creating an army of demon hunters, fel orcs, Nether dragons and enslaved Broken to stave off what he saw as the inevitable return of Kil'jaeden, which was remarkably prescient. He also attacked the Naaru in Shattrath City, which was less intelligent and eventually led to his downfall. With the Naaru's help, the Broken Akama freed Illidan's longtime stalker, Maiev Shadowsong, and they began an operation to take him down from the inside. Akama, Maiev, and yet another group of adventurers finally defeated the misunderstood quasi-demon.
And Kael'thas ... well, props to Blizzard for pulling a bait and switch on this one. At first, it looked like Kael'thas was draining mana from the area of Netherstorm to power Tempest Keep, aid Illidan's plans, and maybe build a new homeland for the blood elves. Then, after some quests, the renegade blood elves known as the Scryers discovered that he had jumped ship on Illidan and started working for the Burning Legion, possibly to get the elves a better magic source. Yay for shortsightedness! Anyway, adventurers yet again stormed Tempest Keep and took out Kael'thas, only to have him announce (once you'd already returned to Shattrath and couldn't go back to finish him off) that he'd survived and would return to be a bigger pain in the ass than ever.
Indeed he did. From what we can see on the test realms, patch 2.4 begins with a bang, as Kael'thas and his groupies sneak into Silvermoon City and steal the captive Naaru that was being used to "power" the blood elf paladins. As such, the blood knights renounce their allegiance to their prince and join up with the Naaru in Shattrath City. Kael'thas and his remaining loyal elves decamp to the isle of Quel'Danas, where they reactivate the powerful Sunwell and attempt to use its energies to summon Kil'jaeden. One presumes that they do not succeed, although it would be totally awesome if they did. "Sorry for all your hard efforts, adventurers, but you were two minutes too late. If only your priest didn't go AFK to get high, you would have stopped the destruction of the world ... but no."
And that's the story of the Burning Crusade.
Also, there was something with trolls.