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. 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 until a Navigator by the name of Joyre Macran accidentally discovered the palace-warship of the Blind King in the Warp. He brings an Emperor-class battleship called the Dominus Astra and blows up the Blind King. Without their leader, the cult is finally ended.
One of the more important events of the Age of Redemption was the Abyssal Crusade. Basically, a Chaos-worshipping Cardinal (apparently such things exist) sent thirty Chapters of Space Marines on a crusade into the Eye of Terror, where most of them went renegade and/or insane, some fought to the bitter end, one chapter's fate remains unknown, and one other chapter survived along with a couple other survivors and made their displeasure known to the heretic cardinal and his followers. What little was left of them (the heretics, not the Marines) was tossed into a star. You could choose to ignore this, of course, as a Chaos worshipper's practices in sanctified territory just... doesn't work the way this implies.
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.