Blank
Blanks are a rare breed of human Psyker, even in the explosive populations of the Imperium and average about 1 or 2 on the average planet of 10 billion inhabitants. They function as anti-psykers, having no warp presence of their own. This makes them seem unnatural to ordinary people in an indescribable way, and anathema to Psykers by shutting off their powers and warp sense. This unfortunately has an effect on some people more susceptible to the warp causing pangs of sickness and confusion. Blanks are supposedly seeded into humanity by the Deceiver, a C'tan god, as a way to counter the powers of the warp in the future. However this was the pre 5th edition Necron fluff, with the release of the 6th edition's TOMB KINGS IN SPEHSS fluff, this is now pretty dubious since humanity hasn't even evolved yet during the age of the Necrons. Though, like with all oldcron fluff, it could be easily explained by the actions of escaped Deceiver shard, or even mega-shard (few shards merged together).
Sisters of Silence
The sisters of silence were one of the most prominent users of blanks in the entirety of the imperium. They were formed by Malcador the Sigillite during the early days of the great crusade to aid the forces of the imperium against some now unknown xenos races who had psykers of their own and used them against them.
During the Horus Heresy the sisters of silence proved instrumental in defeating the Traitor Legions and there large groups of psykers. They were present during the Burning Of Prospero and were vital in silencing the legions ranks of psykers. They did however suffer heavy losses and in the chaos that followed the heresy lost a lot of power and it is unknown now whether the organisation still exists or not. A shame because they could be really valuable against the enemies of the imperium now.
The ultimate fate of most Blanks is to either be picked up by the Black Ships and turned into a Culexus Assassin, be killed by the hubristic citizens of the Imperium due to their rampant xenophobia, or to fed into Kroot to give Tau Anti-psykers. They also used to be turned into Necron Pariahs if ever the Necrons managed to capture a blank. However, with the fluff re-write, not anymore.
Hopes for Necrons, AKA: Possibility of Pariahs Returning...MAYBE
In the current Necron fluff starting from 7th Edition Codex, Illuminor Szeras managed to capture a Culexus Temple Assassin during a surprise incursion against a Chaos held world (see 993.M41 A DARK EXPERIMENT in the current Codex) and trolls the High Lords of Terra into sending more of them (which the old farts comply by sending entire Assassin Execution Forces, though it's not written if those were composed of Culexus Assassins or other types of Assassins).
This may be something of a good thing, since a lot of people actually liked Pariahs and were upset after Matt Ward removed them in favor of the Lychguard.
Reminder: Necron Pariahs were once Blanks that were converted by the Crons as anti-psyker cyborg shocktroopers armed with Warscythes and somewhat as a retinue for Necron Lords. Pariahs were introduced in the 3rd Edition Codex Necrons as an Elite Choice, but were removed in the 5th Edition Codex.
The above incident with Szeras and the Culexus may even be made into a new Pariah Origin Story. Even back in the times when GeeDubs were still cool and their site was still more than a catalogue and had hobby ideas and many more, there was a scenario telling the origin story of how Necron Pariahs came into being as the Necrons had to escort to safety a prototype Pariah (who was de-facto a converted Culexus Assassin who had capabilities of both Culexus AND Pariah and kept his assassin wargear in addition of getting a Warscythe) while protecting him from a Inquisitor and his army.