The War of the Beard (The War of Vengeance)
What Could Possibly Go Wrong?
Before the infamous War of the Beard, the Dwarves and the Elves were at peace. They were re-continuing trade, which made both empires rich-out-of-their-minds. The Dwarfs were at their highest point, the Silver Age. It is in this period that the Dwarfs pretty much kicked Orc ass for SPORT and not for the sake of survival. They also had most of their ancient relics, and Karak-Eight-Peaks, the greatest Dwarf Fortress of all, still standing. The Elves were somewhat dismayed at Malekith's dissension, but hey, they were rich as hell and powerful to boot. But they were still gigantic sissies who cheated the Dwarfs behind their back.
God Damnit, Caledor II
Then the Dark Elves, posing as High Elves, started to mercilessly rape Dwarven caravans. The Dwarf High-King at the time, Gotrek Starbreaker (this manly-ass Dwarf could probably beat Khorne at arm-wrestling and make him look like a pansy in comparison, but he isn't known for his smarts) promptly got pissed and sent over diplomats to yell at Caledor II, the jackass that was Phoenix King of the High Elves at the time. Caledor II proceeded to shave the diplomats of their beards and hair (Hence why the Elves call it, "The War of the Beard"). To Dwarf-kind, this is the greatest crime one can commit. Gotrek Starbreaker, hearing of his, spent a year or so mustering the full, raw, uncut power of the Dwarven kingdom before launching a brutal attack on the Elven colonies in the Old World.
The Actual War of the Beard
The first siege of Tor Alessi began, in which the Dwarves were forced back (but not without wrecking half the city). Caledor II, pissed, marched on down to the Old World and slew Gotrek Starbreaker's son, Snorri Halfhand, in single combat. Afterwards, he raped a giant army of Dwarfs. To be fair, Halfhand was killed by a sucker punch that a wiser Dwarf would've known to avoid.
After Halfhand died, the Dwarves got their act into gear, and began their rape-fest of the Elven colonies. At the battle of Oregor, the Elves were struck a serious blow by the Dwarves in a battle largely consisting of Manoeuvring. Yeah.
In said battle, a cousin to Gotrek Starbreaker named Morgrim marched his bum right through a giant army of elite Elven troops, took Imaldrik, the Prince of Ulthuan, and proceeded to use him as a dishtowel. Dismayed, the rest of the depleted Elven forces ran for their lives. He then got the name "Elgidum" from said battle - which means Elfdoom. Awesome.
After that, the Elves got butthurt and decided to try and attack Karak Azul, where the Dwarf's best smiths resided. They almost won, too, due to superior numbers. But a Dwarf miner nicknamed "The Nightmare of the Deeps" rallied the forces of the Hold and kicked the Elves halfway across the Old World. The High Elves realized that this badass was a pretty big threat, so they sent one of their greatest tactical geniuses to combat him. They fought each other to many costly stalemates until they met eachother inside an Elven Colony. The Dwarfs burnt the city to a crisp by accident, and both forces fled, excluding the two leaders of the armies. Locked in close combat, they killed each other in the middle of the burning city. Some say that in the ruins of the colony, their ghosts still fight, locked in eternal combat. But that's bullshit, since manly Dwarfs who die in combat pretty much always go to Dwarf Heaven.
By then, there had been a great number of sieges on Tor Alessi. Finally, the wall was pretty much completely obliterated, so the Dwarves piled in, slaughtering the Elves cowering within the city. Gotrek, carried upon his throne, found Caledor II trapped in a corner, unable to flee. They fought mano-e-mano for days upon days before Gotrek Starbreaker struck the Phoenix King Caledor II with a single blow from his hammer after he pleaded for mercy, killing him. He then stole his crown, telling the enemy "Nanana boo-boo, i'm better than you, stick your head in doo-doo" and burnt the city down, retreating to Karaz-A-Karak to flaunt his victory. The Elves, utterly demoralized, gathered all of their forces for one final suicidal push on Karaz-A-Karak before word came that the Dark Elves had attacked Ulthuan. They promptly retreated to their homeland, the few left behind becoming Wood Elves (who continue to get annihilated by Dwarfs and Beastmen on a daily basis).
Since then, each faction has had burning hatred for each other. But each faction was made considerably weaker by the war, making them both prone to their fall-from-graces.