Official Canon Edit
Konrad Curze was found alone on Nostramo, a planet plunged in perpetual night. Criminals ruled the hives with an iron fist. Without anyone to raise him, Konrad instead became a vigilant and punished criminals in horrifyingly gruesome displays. Over time he became the legendary Night Haunter, and was made de facto ruler of the planet.
When the Emperor came to his planet, Konrad shrieked in horror and attempted to claw his eyes out, as he saw the deaths of his fathers and brothers - save for Fulgrim, whom he perceived would somehow cheat death.
While Konrad had been given command of the Night Lords, Nostramo once again fell into criminality. And his formerly noble hand-picked marines had been replaced by increasingly psychopathic murderers who reveled in terrorizing their victims. Eventually, Konrad decided that enough was enough, and destroyed Nostramo. His brothers, already concerned with his mental instability, were shocked, and were about to bring him in to justice.
Horus Heresy Edit
Before anything could be done about Konrad, Horus' betrayal became known. The loyalists who gathered on Istvaan III became victims of the Drop Site Massacre, wherein the traitors, now with Konrad among their number, wiped out the Salamanders, Iron Hands, and Raven Guard. Though Vulkan survived, he was given over to Konrad for torture.
Konrad unsuccessfully tried to kill his brother over an over, but Vulkan eventually escaped. Konrad followed him to Ultramar where the other Loyalists gathered, and began a campaign of harassing them to keep them away from Terra. Konrad was eventually captured by Lion El'Jonson, but Konrad had the last laugh when he revealed to Roboute Guilliman what destruction Lion had caused to get to him.
Konrad eventually escaped, but not long after the Heresy ended, he was cornered alone by an Imperial Assassin. Having foreseen this, Konrad allowed her in, as he was done being the Night Haunter. While it is believed that the assassin killed him, there is no confirmation as of yet.
TTS Canon Edit
The Emperor complained that Konrad Curze "couldn't stand a little fucking sunlight, and was constantly feeling persecuted by fantasies of a dark and depressing future."