Age of the Dark Imperium
The Age of the Dark Imperium is one of the major time periods of the Imperium of Man. It was preceded by the Time of Ending, starting in M42. As of Warhammer 40,000 8th edition, it is the "present day" of the setting.
Despite the Imperium being cut in half by the biggest Warp Storm the galaxy has ever seen, the Imperium has rallied around the resurrected Roboute Guilliman, now back in his old role as Lord Commander of the Imperium. While the Primarch has managed to fix a substantial deal of the damage caused to the Imperium by the Great Rift, even he knows that the worst is yet to come.
Noctis Aeterna
Main article: Great Rift
Also known as the Blackness in Low Gothic, the Noctis Aeterna was an event caused by the formation of the Great Rift where the light of the Astronomican vanished and Daemonic incursions ran rampant. The event appeared to distort time itself, lasting a few days on some planets, while on Terra it lasted for just over a month. (And it's speculated that it's still going on for some unfortunate planets.) Judging by the time-frame presented in Watchers of the Throne: the Emperor's Legion, the Noctis Aeterna began a few months after the Fall of Cadia and partway through Roboute Guilliman's voyage to return to Terra, although the aforementioned time distortion means it is only an accurate timeline from Terra's perspective. From Baal's perspective, it only lasted a day or two, yet when it cleared up the Blood Angels had discovered that seventy years had passed in the outside galaxy. The event culminated in an army of Daemons of Khorne invading Terra itself. While this was repulsed thanks to Guilliman and the Custodes, the attack still shook the Imperium to its core as it proved that the influence of Chaos was stronger than ever before and that even the Throneworld was no longer safe from its reach.
The consequences of this left major scars that have still yet to heal. The Imperium lost contact with half of all known Space Marine Chapters, and twelve chapter homeworlds were confirmed to be destroyed. Every Eldar Craftworld was assaulted by Chaos forces (including the ones hidden in the Webway), and they have yet to account for the fate of two of them. Armageddon was transformed into a half-Daemon World, turning the war between Orks and humans into a four-way clusterfuck as Daemons of Khorne and Tzeentch joined in on the fun. On the positive side, the Blackness unintentionally managed to save the Blood Angels, as it allowed Ka'Bandha to destroy the tendril of Hive Fleet Leviathan attacking Baal as the Great Rift dragged many of the Hive Fleet's bioships into the Warp.
From this point forward, attempts at forming an objective chronology become increasingly pointless due to the continuing time distortions across the galaxy; most worlds end up using the formation of the Great Rift as their new "Year Zero" as a result.
Indomitus Crusade
Big G's first military campaign after crowning himself the Lord Commander of the Imperium. The Indomitus Crusade was aimed at shifting the Imperium into the offensive after the damage done by the 13th Black Crusade by going into the stranded "Dark Imperium" and try to liberate as many besieged Imperial worlds as possible, while exterminatusing those unable to be taken. Additionally, the other objective is simply to kick Chaos out of their lawn and try to re-establish some form of order in the Imperium so Guilliman can begin to fix what's left of it.
Aiding him here are whatever Imperial forces he could muster, dozens of space marine chapters, and the Primaris Marines, Daddy Cawl's pet project.
By the end of the Crusade, Chaos' momentum had effectively been destabilized and halted, but the damage has been done. Hundreds of Imperial worlds have either been destroyed or corrupted beyond measure and while Chaos' advance has been stalled for the moment they're still causing trouble for the Imperials. On top of that, much of the "Dark Imperium" is still cut off from the Astronomican and is generally defenseless.
Overall, Guilliman stopped the Imperium from bleeding to death, but now he has to contend with a nasty infection from the wound. Still, you can nurse a sick man back to health, but you can't do anything anymore once he's dead.
Speaking of infections and sickness, during the confusion Nurgle's armies invade Ultramar, forcing Guilliman to return to defend his home system.
Ultima Founding
Cawl's Primaris Marines are used to reinforce a number of Marine Chapters to get them back into optimal fighting strength, while some new Chapters composed entirely of Primaris Marines are also founded.
The Emperor's finest are gearing up for some dark times ahead.
Plague Wars
Nurgle's offensive into Ultramar. Using the Scourge Stars as a staging area, Mortarion led Nurgle armies in a bloody campaign to annex Ultramar into Nurgle's realm. The home team is led by none other than Grandpappy Smurf himself (also a reason he had to cut the Indomitus Crusade short).
The war was decided in The Battle for Konor, which saw Mortarion being pushed back but at a great cost; dozens of worlds were either destroyed or corrupted beyond salvation. Morty would have probably went in for another go, but because most of Nurgle's forces were sent on his campaign the other Chaos Gods decided to invade the Scourge Stars for shits and giggles. As a result, the Plaguefather had to call Mortarion back to deal with his rivals. In light of the new threats that they face, Guilliman charges its new Tetrarchs with expanding Ultramar's borders, the better for pushing back any future attacks.
War of Beasts
Centered on the world of Vigilus, it's more or less the Imperium's desperate attempt to keep a vital foothold in the Dark Imperium in Mankind's hands. Initially it was just a campaign to repel an unexpected Ork invasion, but soon exploded into a massive free-for-all when a Genestealer Cult-led rebellion threatened to undermine the planet's defenses. What's more, Dark Eldar raiders stalk the underhive, while Chaos-tainted madmen and the Death Guard make their presence known all-too soon.
And now the conflict has drawn the attention of Abaddon the Despoiler's Black Legion...
The initial phases are described in the Vigilus Defiant campaign supplement, and referenced in the Speed Freekz and Tooth and Claw boxed sets.