It's hard to imagine what the Blue Dragonflight was like before the War of Ancients. Malygos and his consort Sindragosa ruled over a dragonflight as expansive as any, in a world with few if any threats to them. It's clear that Malygos and his flight didn't feel particularly threatened by the wars between the troll and aqir empires, nor were they particularly concerned with the rise of night elf society on the shores of the Well of Eternity. At least, they weren't concerned enough to actually do anything about it. There are no reports of the blue dragons approaching the night elves' highborne and trying to convince them to stop meddling with the arcane power of the well.
However, when the dragons were finally roused to oppose the coming of the Burning Legion via the Well of Eternity (due to Sargeras' influence over the minds of Xavius and later Queen Azshara herself) Malygos made the mistake of being too trusting of his long time friend and fellow Aspect, and it was Malygos who helped convince the other dragons to lend their power to the forging of what was then known as the Dragon Soul. "It is a weapon like no other. It must be like no other." When Neltharion turned the Dragon Soul against the other dragonflights, the blues were the first to pay the ultimate price, as Neltharion froze all of the dragons in place using the power they themselves had donated to his great and terrible artifact. Horrified and enraged, Malygos led the charge against his brother aspect as soon as he was freed, and it was as they moved to attack the insane earthwarder that the blue dragonflight was almost entirely slaughtered. Sindragosa, prime consort to the Aspect, was hurled miles away to the north of the continent of Kalimdor (this was before it was shattered into the three continents of modern day Azeroth) and crashed to the ground in what we today call Icecrown, too weak to even make her way to the Dragonblight where dragons go to die.
Only Malygos and a few others survived, and them only barely behind the Aspects powerful protective magics. The loss of his mate and most of his children and the fact that it was in great measure due to his own work to help convince the other aspects to cooperate with Neltharion broke Malygos' mind, and he and the surviving blues quit the battle. After the Sundering, when the remaining red, green and bronze dragons created Nordrassil to help disguise the new Well of Eternity created by Illidan Stormrage, Malygos appears to have created Mazthoril and set the few remaining blues and blue dragonkin there to guard over the magical power slumbering below the World Tree. (It's possible also that Mazthoril was created far later.)
Afterwards, Malygos retreated to his lair in Coldarra, going so far as to rip the place away from the land to help ensure its isolation. Having lost so much and now finding their Aspect descending into brooding insanity, the few remaining blues were unable to stand up to Deathwing and his black dragon forces, and many more were slaughtered in combat against the blacks. The war of dragon against dragon that followed pitted red, blue, bronze and green against black and led to the near extinction of both the black and blue dragonflights and the great reduction of the others. From this point on, dragons could no longer muster the forces needed to truly fulfill their ancient charges, and the age of dragons came crashing to a close.
Yet, despite Malygos' ruin and their incredible losses, the blues did not wholly vanish. Some of them even attempted to pursue their mandate to watch over the world's magic. During the War of the Shifting Sands, for instance, the blue dragon Arygos, son of Malygos and presumably either Sindragosa or her replacement Saragosa (we have no idea when Malygos took a second consort, he may even have had two the same as Alexstrasza did for a time) ended up trapped within the Temple of Ahn'Qiraj alongside equally prominent red and green dragons. Arygos sacrificed himself to ensure that the barrier that trapped C'thun for a thousand years was created, and remained within the structure as a prisoner until mortal adventurers slew C'thun's physical manifestation.