Dalamud
Dalamud was a satellite originally created by the Allagan Empire, however it is most well known for being the harbinger of destruction that was Bahamut. Used by the Garlean Empire as a means to "Free Eorzea of it's taint", it was unclear the amount of untold devastation that would be wrought across the land.
Creation
At the end of the War of Meracydia, the dragons, with the help of the Ascians, managed to perform one of the first recorded summons to revive Bahamut. While what returned was simply a shell of what the great wyrm had been, it nevertheless brought its full destructive force to bear against the Allagans, and was almost enough to turn the tides of war. However, in the eleventh hour, the Allagans managed to reverse engineer the summoning and were able to trap it and connect it to their technology, greatly empowering their warmachina and winning them the war.
Xande, the revived Allagan Emperor, could not be sated by the victory of war, however, and wished to feel the thrill of death once more, as nothing could compare. He commissioned the creation of a device large enough to seal Bahamut and launch into space, where Bahamut's natural Fire-aspect would serve to draw energy from the sun in a much greater capacity than the feeble rays captured by the Crystal Tower. And so, the device was built, and connected to the tower to harness the energy the great wyrm would gather, and successfully launched.
Indeed, it was evident the satellite was capable of gathering energy on a scale unseen before, but the reason why it was being gathered shocked those who worked on the project; it was to be harnessed to open a portal to the Void where the Cloud of Darkness could be summoned to rain destruction down upon the Empire, and the world.
When news of this broke to the people, there were several uprisings, hoping to reach the Emperor before he could activate the satellite and open the portal. However, Xande had thought to activate it remotely, and did so, firing the energy directly into the tower.
While the tower had been reinforced to withstand the massive wave of energy, the ground it stood upon had not. This ended up collapsing the entire Empire into the earth, and setting in motion the Calamity of Earth. With the Empire destroyed, Dalamud continued to float in orbit, gathering energy and harboring an increasingly vengeful Bahamut that no one would see again for millenia.
Project Meteor
The Garlean Empire happened to discover Dalamud almost entirely by chance. Once they discovered it and what it potentially was, the Empire set about trying to communicate with the satellite. Using other Allagan technology, the project dubbed Project Meteor took place at the Bozja Citadel. However, disaster struck, as upon communicating with Dalamud, it fired a single concentrated beam of energy that had been gathered over five thousand years, and obliterated not only the Citadel, but the entire surrounding city in an instant. The Emperor deemed the power too unpredictable, and ordered the project to be shut down immediately.
Nael van Darnus however, had become obsessed with both the Allagan Empire and the project, and wasn't about to destroy all his work. and so he hid the project for over a decade, until at last he was deployed to Eorzea, and used the stalemate there to convince the now aged Emperor to resume the project to "cleanse" Eorzea of its Primal issue. The Emperor agreed, and the project was finally resumed.
While the Eorzeans struggled with Primals, the Empire quickly built Castrum Novum, which housed a recreation of the communicator used a decade prior. Although Cid nan Garlond had learned of the communicator from stolen documents, he learned that the device was already operational, and was slowly pulling Dalamud towards the earth.
A team of adventurers set out on a massive mission with the Grand Companies of Eorzea to lay siege to the castrum and destroy the communicator. Though it was an intense battle, Eorzea succeeded in destroying the device and the Castrum.
Unfortunately, the device's destruction came too late; Dalamud still careened towards Eorzea. As the moon fell, large crags were observed in the land, with a large beacon emitting a beam of light. This was the remnants of an Allagan device that continued to pull the Lesser Moon ever closer.
The Seventh Umbral Calamity
Even after defeating the White Raven and stopping the Allagan device, Dalamud crept ever closer. It was at this time the Eorzeans, at the behest of Louisoix, would set forth and invoke the power of the Twelve to gather enough energy to stop the falling satellite.
At the same time, Nael van Darnus' VIIth legion marched on Eorzea, to Carteneau, to stop any who wished to forestall Dalamud's fall, and see their masters plan to fruition.
And it was there, on Carteneau Flats, the armies of Eorzea and the then Warriors of Light would once again clash with the Empire in bloody battle. The end of this fight was in favor of no one, however, as what happened when Dalamud broke through the clouds, no one could have predicted.
Hanging low in the sky, Dalamud suddenly flashed and cracked open, raining massive shards and fire down below, and from the flames emerged Bahamut, who had harbored rage and hatred for man for several millennia. The wreckage from the satellite would have caused enough damage, but the hell that rained down upon Eorzea that day changed the land forever.
The war forgotten, everyone began attempting to flee to save themselves, but it was of little use. Only a few present that day were able to escape, thanks to Louisoix harnessing the energy of prayer and moving them away from the battlefield.
To this day, the scars of destruction from both Bahamut and Dalamud can be seen across the land, especially at the epicentre in Carteneau, where, thanks to the destruction, large amounts of Allagan technology has been uncovered, and is now the object of battle for the Grand Companies.
The events of the Calamity are visualized in "The End of an Era" and "Flames of Truth" cinematics. "The End of an Era" plays upon first beginning the game on a new Adventurer, while the "Flames of Truth" is part of the post 
The Final Coil of Bahamut - Turn 3 quest cutscenes.