Age of Redemption
Basically, the Imperium, fresh off the Thorian Reformation, decided to expend all of its troops in penitent and redemptive crusades instead of actually defending its borders. This would prove to be a bad idea... at least, if you listen to the core rulebook. The writers seemed to have goofed: the Adepta Sororitas fluff states these were Wars of Faith, which are called by the Ecclesiarch and only include the Adepta Sororitas and whoever else wants to join them (ie it's not mandatory). Theoretically, this means that the Imperium should be better off than it was pre-Apostasy (Sisters burn xenos, don't burn loyal citizens), but apparently this wasn't true.
Sometimes mentioned in fluff relating to the Adeptus Mechanicus, the Occlusiad was a time period when a radical sect of Tech-Priests calling themselves the Apostles of the Blind King (probably no relation to the Silent King) declared humanity to be an affront to the Machine God. Then for good measure, they uncovered a bunch of archeotech that lets them blow up stars (along with some super-strong Great Crusade-era Space Marine tanks, which they could build and deploy en-masse). This actually is more likely than it seems: considering how often the Adeptus Mechanicus priests/generally everyone go insane, it's not so unlikely that one of these rogue sects would manage to get their hands on world-ending technology. Probably a lesson to be learned here somewhere.
War between the Imperium and the Apostles raged for a decade, seeing the outer edges of Segmentum Obscurus purged by exploding stars and traitor Skitarii macroclades. Though the Imperium fought long and hard against the heretic forces (the newly-formed Dark Hunters even managing to hold their own against a massive invasion of Daemon Engines and at least one Titan), the Blind King's psychic foresight allowed the cult to stay a step ahead of their opponents.
Eventually, however, a Navigator by the name of Joyre Macran accidentally discovered the palace-warship of the Blind King hidden in a fold of Warp-space. He escaped and returned, bringing with him an Emperor-class battleship called the Dominus Astra and promptly shows the Blind King the business end of its fuckoff-huge guns, pretty thoroughly killing the Blind King. With their boss dead, the cult is soon isolated and destroyed to the last.
One of the more important events of the Age of Redemption was the disastrous Abyssal Crusade. Basically, a super influential Cardinal and Living Saint named Basillius the Elder sent thirty Chapters of Space Marines accused of being Chaos-tainted on a penitent crusade into the Eye of Terror, where most of them went renegade or traitor, although a few fought to the bitter end and the fate of one other chapter remains unknown. Only the Vorpal Swords escaped the Eye of Terror to make their displeasure known to the cardinal, who was revealed to be a heretic and agent of Chaos.
The Inquisition promptly executed him and put all his treatises, relics, and followers into a cargo freighter and shot them into a nearby sun, then had him pretty much wiped from Imperial records. While no-one remembers the old coot in the present day, it's impossible to ascertain how far his corruption reached and what remnants may remain even in the present day.
In true GeeDubs fashion, despite the massive losses of Space Marines and the creation of a couple dozen Chaos warbands providing massive story fodder, the Abyssal Crusade has never been really elaborated upon beyond throwaway references and one Ultrasmurfs-focused novel in which a Judged warband re-appears to eat shit and die at the smurfs' hands.
A bunch of optimists, mostly children, decided they could change the galaxy for the better with love and tolerance. They decided to go on a pilgrimage for Terra, calling themselves the Children's Crusade.
They reappeared almost a thousand years later, most of the ships twisted and torn beyond recognition. It was renamed the Lost Crusade, and the Inquisition tried their hardest to cover it up (why they didn't use it as an example of why hope over faith in the Emperor is bad is kind of weird). It's almost as though blind optimism and hope attracts negative warp entities.
The BRB gives the title "Dissidence Dreams" to the whole event, but it's not clear why.