Age of Redemption
The Age of Redemption is one of the major time periods of the Imperium of Man. It was preceded by the Age of Apostasy and followed by the Waning, stretching from mid-M37 to the beginning of M39.
Basically, the Imperium, fresh off the Thorian Reformation, decided to expend all of its troops in penitent and redemptive crusades instead of, you know, actually defending its borders. This would prove to be a bad idea. Although, the writers appear to have goofed. The fluff states that these were "Wars of Faith". Fluff also states that a war of faith is declared solely by the Ecclesiarch and only includes Ministorum military forces. In other words, the Sororitas and no one else. This means that the Imperium should be better off than it was pre-Apostasy (xenos get burned by Sisters and Sisters eventually would get wiped out, so they can't burn anymore loyal citizens just because they want to). Sure, there were some crusades, too, but it was mostly wars of faith happening during the Age of Redemption.
The Occlusiad
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, declare humanity to be an affront to the Machine God. Then, for good measure, they uncover a bunch of archeotech that lets them blow up stars. Because of course they do.
War between the Imperium and the Apostles rages for a decade until a Navigator by the name of Joyre Macran accidentally discovers 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.
Abyssal Crusade
One of the more important events of the Age of Redemption was the Abyssal Crusade. Basically, a Chaos-worshipping Ecclesiarch (apparently such things exist) sent thirty Chapters of Space Marines on a crusade into the Eye of Terror, where most of them went renegade.
Children's/Lost Crusade
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.
And then all the ships got lost in the Warp!
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.