Peverell family

Peverell was the surname of a medieval pure-blood wizarding family. Hermione reported in early 1998 that, according to Nature's Nobility: A Wizarding Genealogy, the Peverell name was among the first to "become extinct in the male line," meaning that the name had died out among wizarding families.

The Three Brothers

Hallows Sign — The sign of the Deathly Hallows, mistakenly called the "Peverell coat of arms" by Marvolo Gaunt

"And Death spoke to them. He was angry that he had been cheated out of three new victims, for travelers usually drowned in the river. But Death was cunning. He pretended to congratulate the three brothers upon their magic, and said that each had earned a prize for having been clever enough to evade him."

— Excerpt from the The Tale of the Three Brothers, which is believed to be based on the Peverell brothers^[src]

The Peverell brothers, Antioch, Cadmus, and Ignotus, are believed by some to be the subjects of the wizarding legend, "The Tale of the Three Brothers."

Each possessed one of the Deathly Hallows:

Antioch: the Elder Wand
Cadmus: the Resurrection Stone
Ignotus: the Cloak of Invisibility

According to legend, Antioch's throat was slit in his sleep the night after winning his first duel with the Elder Wand. He had boasted of its power, and someone coveted the wand enough to kill him for it. It is unknown if Antioch was really murdered, though given the Elder Wand's violent history it seems likely, or if he had any descendants.

The legend also says that Cadmus committed suicide after using the Resurrection Stone to bring back his beloved (who had died an untimely death), having found the experience completely unfulfilling. Not only was Cadmus's beloved an echo of herself in life (q.v. Harry's parents, Sirius Black and Remus Lupin as they appeared to Harry before facing Voldemort in the Forbidden Forest), she found the world of the living uncomfortable and wished to return to the afterlife. However given the Gaunts appear to be descended from Cadmus, as they possessed the Stone, it would seem Cadmus lived long enough to at the very least sire children.

Apparently, Ignotus lived a long and fulfilling life, and, having decided to elude Death no longer, passed the cloak on to his own son. He joined Death and welcomed him as a brother. His lineage is the easiest of the brothers' to trace, as the cloak would continue to be handed down from parent to child through the generations finally coming into Harry's possession.

Dumbledore believed it far more likely the three Peverells were the creators of the Hallows and the legend to be merely a story partially inspired by their nature, which would accout for how Cadmus sired a child despite the legend implying he comitted suicide relatively soon after obtaining the stone.

Descendants

The Peverells had numerous descendants through female lines, but by the twentieth century only two such families could be identified through heirloom.

Gaunt family

"Marvolo Gaunt was an ignorant old git who lived like a pig, all he cared about was his ancestry. If that ring had been passed down through the centuries, he might not have known what it really was. There were no books in that house, and trust me, he wasn't the type to read fairy tales to his kids. He'd had loved to think that scratches on the stone were a coat of arms, because as far as he was concerened, having pure blood made you practically royal."

— Harry Potter on Gaunt's ignorance of the Hallows, despite possessing one of them^[src]

Marvolo Gaunt claimed Peverell blood through the female line, and had a ring with what he claims is the Peverell crest, which actually was the sign of the Deathly Hallows. This ring was set with the Stone of Resurrection, and later became one of Voldemort's Horcruxes .

Potter family

According to Harry's near-death vision of Dumbledore, Harry too is a descendant of the Peverell line through his father James Potter, and hence Ignotus' cloak is rightfully his.

1997-1998 Quest for the Hallows

During the Horcrux hunt, Harry Potter, Ronald Weasley, and Hermione Granger began to encounter a mysterious sign, rather like a triangular eye. Harry first saw the symbol worn by Xenophilius Lovegood at the wedding of Bill Weasley and Fleur Delacour the previous summer, but it later was seen in The Tales of Beedle the Bard that Dumbledore left Hermione in his will. In addition, Hermione located and showed to Harry the grave of Ignotus at the graveyard in Godric's Hollow on Christmas Eve, 1997. The symbol engraved on the headstone was the sign of the Hallows as well. After Ron rejoined them, they visited Xenophilius and questioned him about the symbol, which he said was the emblem of the Deathly Hallows. Harry soon remembered he had heard Marvolo Gaunt mention the name "Peverell" to describe the coat of arms on his ring (also the sign of the Hallows) during Bob Ogden's memory he saw in the Pensieve during his private lessons with Dumbledore.