There will be spoilers for every patch of Mists of Pandaria, including 5.4 and the Siege of Orgrimmar raid, in this post
Leaving aside blame for a moment, let's just look at the results of the past year or so in terms of what actually happened. To heavily summarize events:
Horde and Alliance forces discovered Pandaria, landing in the Jade Forest.
Both factions mobilized local allies (the Horde made pacts with the Hozen, the Alliance joined forces with the Pearlfin Jinyu) and waged a proxy battle through these cat's paws. The result was the desrtuction of the Jade Serpent's next incarnation and the release of the Sha of Doubt, leading to the Sha infestation of the Temple of the Jade Serpent.
Both factions pushed onward into Kun-Lai Summit, where they fought the yaungol and set up base camps, converting local pandaren to their cause. They did not actually join in battle at this time.
Scouts and agents of the Horde and Alliance penetrated deeper into the continent, in time exploring the Townlong Steppes and Dread Wastes. In time these advance forces even managed to convince the August Celestials to allow both the Horde and Alliance to set up bases within the sacred Vale of Eternal Blossoms.
Both the Horde and Alliance made large-scale military bases in the Krasarang Wilds and began using these to wage resource war against one another, fighting over territory and raw materials as well as ancient mogu artifacts buried below the surface of the wilds.
This period of hostilities led to a culmination wherein Warchief Garrosh Hellscream attempted to use a mogu artifact, the Divine Bell, to infuse his own soldiers with the power of the Sha. The fallout from this action caused the neutral Kirin Tor to eject the Sunreaver pro-Horde faction from Dalaran and declare themselves for the Alliance under their leader, Lady Jaina Proudmoore. Prince Anduin Wrynn nearly died in the attempt to destroy the Divine Bell, which succeeded. Garrosh Hellscream, however, was not balked from his goal of finding a new weapon.
There's more, of course. Things had only begun to heat up at this point.
After the destruction of the Divine Bell, the lines were drawn - former allies in neutral Dalaran were now bitter enemies, and each served one of the two factions making war on Pandaria's shores. But they couldn't immediately turn on one another.
The Sunreavers and Kirin Tor lead expeditions to the Isle of Thunder when the Shado Pan defenders of Pandaria become alarmed at the increasing strength of the Zandalari trolls and their mogu allies. What was first hinted at in the northern islands off the coast of Kun-Lai becomes verified fact - the ancient Lei Shen, Thunder King of the mogu and first mogu emperor of what is now Pandaria, lives again. In an attempt to defeat the Thunder King before he could call all of Pandaria's mogu to his service (and also, both Sunreavers and Kirin Tor sought powerful weapons of their own to use against Garrosh) these forces summoned champions from their respective factions to storm into the labyrinthine Throne of Thunder and kill the resurrected Thunder King. They succeeded, but Hellscream was not idle during this period.
Assassins loyal to the Warchief attempt to assassinate Vol'jin, leader of the Darkspear trolls. Only the action of three Horde heroes prevent his death, and he goes into hiding to plan his next move against Hellscream.
Alliance forces under King Varian Wrynn drive the Horde from the Temple of the Red Crane without undue damage to the temple itself. Varian follows this victory by then bringing the dwarves of Ironforge news that the Zandalari are on the move, and with the help of Moira Thaurissan's Dark Iron Dwarves foils a troll uprising. These actions bring the Alliance closer to a unified front.
During all of this, the black dragon scion Wrathion, the self-proclaimed Black Prince, was amassing power of his own and manipulating mortals to help him accumulate it. In time, he would come into possession of the very heart of raw Titan power that Lei Shen in turn once stole from the mysterious Ra-Den. As time progressed, Wrathion tested the resolve of both Horde and Alliance, seeking to determine which faction deserved to rule over all Azeroth - for he believed only a united Azeroth could stand against what was to come.
While the Thunder King was being dealt with, events progressed elsewhere. Seeing the Shado-Pan distracted, Hellscream began a vast excavation project in the heart of the sacred Vale of Eternal Blossoms. This project led to a terrible discovery. At the same time, Vol'jin begins his revolt against the Horde, the Darkspear Revolution. Seeking to take advantage of the situation, SI:7 operatives on the ground elist a handsome draenei to offer the revolution an temporary alliance of shared purpose - they would work together to supply Vol'jin's forces for the ultimate push on Orgrimmar.
Garrosh was not caught off guard by this turn of events. Instead, the Warchief of the "True Horde" (those forces that had stayed loyal to him, primarily orcs) led an assault on the Shado Pan for the purpose of showing the world his true power. The discovery from beneath the Vale was the terrifying Heart of Y'Shaarj, a remnant of a dead old god slain by the Titans at the dawn of time whose final breath created the Sha and left the mantid without a god to worship. Defeating Taran Zhu in pitched battle, Garrosh threw the Heart into the magical waters of the Vale, in an instant defiling them with raw corruption that dwarfed even the power of the Sha themselves.
This final atrocity brought the situation to a head, just as Hellscream had hoped. The Darkspear Revolution brought all of its forces to the gates of Orgrimmar, while the Alliance prepared to storm Bladefist Bay alongside the Sin'dorei and Forsaken fleets. A cadre of brave heroes aided Lorewalker Cho in stemming the immediate corruption of the Vale, striking down the last and greatest of the Sha, the Sha of Pride, who had been summoned to the chamber where Y'Shaarj's Heart had lay dormant by the combination of its progenitor's raw naked power and the staggering hubris of Hellscream, who in his pride abandoned even Gorehowl in favor of a copy made for him by the Old God's still-beating Heart. Once the Sha of Pride was defeated (costing the life of Norushen, the ancient Titan Watcher who'd held vigil over the chamber for ten thousand years) this squad of some of Azeroth's most powerful champions made their way to assist in the seizure of Orgrimmar and the final battle with Hellscream.
The Warchief proved too far gone to negotiate with. Months of effort had provided him with a vault-like sanctuary below the surface of the city, hollowed out of the former Ragefire Chasm. Within its walls, Garrosh had assembled a host of weapons, treasures and even creatures from Pandaria itself which he intended to use to crush all opposition. Furthermore, the Klaxxi Paragons, sensing the Heart of Y'Shaarj, came to Orgrimmar to reaffirm their worship of the Old God and its superiority to the Titans. Against all this, the heroes of Azeroth ultimately prevailed and struck Garrosh Hellscream down. In defeat, Hellscream was shown mercy that he himself would or could not, and was taken into confinement to be tried for his actions. The Horde chose a new Warchief, and the Alliance chose to cease hostilities... for now.
This brief and necessarily incomplete summary of events still manages to convey that, in the space of a year, the strangled hostilities of the Cataclysm that ended in the destruction of Theramore rapidly and repeatedly escalated. At the beginning of the year, despite the attack on Theramore, Garrosh Hellscream was indisputable in his role as Warchief of the Horde and even his strongest detractors, Vol'jin and Baine, accepted him as ruler of the Horde.
Meanwhile, after her ascension to head of the Kirin Tor, Lady Jaina was still committed to neutrality and peace, albeit all who knew her knew that she had been sorely tempted to simply attack Orgrimmar with the Focusing Iris and wipe it off the coast of Durotar. It took Hellscream less than a year to shatter the Horde's unity, push Jaina past the brink and into a committed role standing firmly with the Alliance (a move that dragged Dalaran out of the neutrality it held during the Scourge Invasion and Nexus War), and motivated Varian Wrynn to finally find a way to unify the Alliance. The destruction of the Pandaria campaign was mostly confined to the new continent - the Pandaren were forced to see the destruction of the Serpent's Heart and, as if to drive the point home, the even greater devastation of the Vale of Eternal Blossoms and the life giving waters that sustain Pandaria's farmland - and while those waters were cleansed of corruption with the restoration of Immerseus and defeat of the Sha of Pride, the aftermath will be long felt.
And all of that in the space of one year.
While you don't need to have played the previous Warcraft games to enjoy World of Warcraft, a little history goes a long way toward making the game a lot more fun. Dig into even more of the lore and history behind the World of Warcraft in WoW Insider's Guide to Warcraft Lore.