Phaeron

I find your lack of faith....disturbing...

A Phaeron (male) or Phaerakh (female) is a Necron who rules an entire Necron Dynasty; after the Triarch left the galaxy following the War in Heaven, they are the highest-ranking Necrons in the galaxy, barring the Silent King himself.

Because the Necrontyr were so short-lived, there used to be a fair amount of turnover in this position (and in all positions in Necrontyr society, for that matter), but after the pact with the C'tan and biotransference, the present set of Phaerons are effectively immortal and ever-living (in fact, they have a special rule called just that), so the only way to replace one is to kill him or conquer his dynasty. Either one is a difficult proposition, as the Phaerons were given bodies of the finest, most robust construction, and rule over endless phalanxes and legions of warriors. However, this does nothing to prevent all manner of civil wars and political shenanigans as various nutty robot zombie nobles attempt to seize power for themselves.

They wear the most esteemed of Sempiternal Weaves to denote their rank and carry similar equipment as their lesser Overlord counterparts, although certain Phaerons such as Tollzyn the Incurious and Imotekh the Stormlord could carry around their own unique staves like the Empathic Obliterator and the Staff of the Destroyer respectively, as well as a Gauntlet of Fire to throw Hadoukens, just to flex.

Phaerons were added to the Necron army in the Fifth Edition Codex, as a way to give the Necrons some character. Note the pun on "Pharaoh," the ruler of an ancient Egyptian dynasty, as if you needed more proof that the new Necrons are Tomb Kings IN SPACE.

Phaemous Phaerons

• Szarekh, the Silent King, Phaeron of the Szarekhan Dynasty, the only surviving member of the Triarch and one-time ruler of the entire Necron Empire. After defeating the C'tan, he left the galaxy out of shame that he fed his people's souls wholesale to the Deceiver, met the Tyranids, and hustled back home to rouse the Necrons against the extragalactic threat. The other two phaerons of the Triarch, Hapthatra the Radiant and Mesophet the Shadowed Hand stand at either side of the Silent King upon the Dais of Dominion.
• Imotekh the Stormlord, Phaeron of the Sautekh Dynasty, the most powerful Dynasty as of the 41st Millennium.
• Xun'bakyr, Phaerakh of the Maynarkh Dynasty, who's noted to have literally destroyed a C'tan out of existence.

Tabletop

Phaerons on the tabletop are basically Necron Overlords with an extra upgrade that makes them (and any unit they join) Relentless. In 5th this was an improvement, making your I2, 1-attack zombiebot horde suck slightly less when push came to shove. In 6th, assault was essentially worthless, so there's no real point in doing this. Unless you WANT to assault with warriors (pro-tip: don't bother).

In 7th Edition, you can't make an Overlord a Phaeron anymore. At all. Crunch-wise, it's no big deal (Relentless wasn't actually needed that much). Fluff-wise, you can just call your Overlord a Phaeron all the same.

EDIT: GW has heard our pleas, returning Phaerons to the tabletop as an upgrade as of ninth edition, this time in the form of a two CP upgrade that allows them to My Will Be Done twice in a single turn!