Silent King
"He is the Breaker of Gods"
The Silent King is the ruler of all Necrons, though in the 41st millennium his influence is starting to dwindle. Back when the Necrons were still the Necrontyr, it was a hereditary position occupied by the ruling member of the Triarch (which was itself composed of three Phaerons of powerful Dynasties). The name was derived from the tradition that the Silent King never spoke to his subjects, instead letting the other two Triarchs speak for him.
The big S.K. is intended to be a background "ghost" character; to reinforce this, GeeDubs deliberately never gives him official artwork, much less a model and stats.
Szarekh, The Last Silent King
The last Silent King was named Szarekh, and it was he who sealed the pact with the C'tan in order to gain their power to fight against the Old Ones. Unfortunately for the Necrontyr, there was a catch: the bio-transference process that upgraded them into the metallic, immortal Necrons had the side-effect of stripping them of their souls and, for the most part, their free wills. The Silent King was placed in charge of the entirety of the Necron race, while the delicious souls went to the C'tan.
Szarekh was not happy about this (though he wasn't precisely angry either, given the loss of his soul), but he had no leverage to fight the C'tan -- what they had given, they could easily take away, and then some. Therefore, he fought the War in Heaven alongside the C'tan, and waited until the very moment of victory, when the C'tan were nearly spent, and turned on them with every warrior and weapon at his disposal, shattering the star-gods and binding the fragments that remained. But somehow he forgot to go after the most powerful one.
The War in Heaven left the galaxy a mess, and Szarekh decided that most of it was his fault, so he commanded the legions to rest in their Tomb Worlds to let the galaxy heal for the next sixty million years, relinquished control of the Necron nobles, and exiled himself from the galaxy. His last instruction was to rebuild the Necrontyr Empire and return to flesh bodies, though how this happened was left up to any Phaerons who could make it happen. Szarekh then left for the intergalactic void, vowing to never return to the Milky Way...
...which lasted right up until he found out what was in the void: the Tyranids. When he encountered the vanguard of Hive Fleet Behemoth, he NOPE'd right back home, getting in touch with the remaining Praetorians to awaken every Tomb World still standing and unite against the swarm -- after all, if the Tyranids ate everything, there would be no bodies to return to, and nothing to rule over! The Silent King so disliked this possibility that he allied with the Blood Angels to fight off a Tyranid landing force, and even let them go on their way when the fighting was over.
Going by the description in "The Word of the Silent King", the Silent King wears a Sanguinius Death Mask.
Also, he'll be back really soon with the reveal of 9E. From what little we've seen of his new model so far, it's likely that he's going to be accompanying an entire retinue, not unlike another influential bone-daddy, and will be carrying a C'tan shard of his own.
Speculation
During the Alliance negotiations with Dante, the Silent King mentioned a similar conversation with their Primarch, Sanguinius. This would mean that Szarekh had already returned 10,000 years before the 1st Tyrannic War and one of the Primarchs was aware of the Tyranid threat. Common sense dictates that this happened just before it all went to shit and all the humans involved got killed (or sat on the Golden Throne) before spreading the alarm.