Who are the Wild Hunt
The Wild Hunt is the elite cavalry of the Aen Elle (Alder Folk), a group of elves from a parallel world. They are not the same species as the Aen Seidhe, the elves who live on the Continent. Formally called the Dearg Ruadhri (Red Riders), the Wild Hunt appears in other worlds as spectral horsemen, giving rise to legends and folklore across multiple dimensions.
The Gate of the Worlds
The Aen Elle once controlled the Ard Gaeth (Gate of the Worlds), which allowed them to travel between dimensions in large numbers and conquer other worlds. After the Conjunction of the Spheres, they lost control of the Gate. To compensate, they developed navigators, specialized mages who could open small portals. But these portals could only transport a handful of riders at a time, severely limiting their power.

The Wild Hunt's ultimate goal was to recapture someone with the Elder Blood gene who could reopen the Gate and restore their ability to invade other worlds at will.
Eredin Breacc Glas
Eredin was the commander of the Red Riders and later crowned himself King of the Aen Elle. He was ruthless and ambitious. In the novels, Eredin murdered King Auberon Muircetach by poisoning him with an overdose of an aphrodisiac, seizing power for himself. His obsession with the Elder Blood drove the events of The Witcher 3.
In The Witcher 3, Eredin is the final boss of the main storyline. His generals include Imlerith (killed by Geralt and Ciri at the Battle of Kaer Morhen), Caranthir (the primary navigator), and Ge'els (who can be turned against Eredin through diplomacy if Geralt exposes Eredin's regicide).
Connection to Ciri
The Wild Hunt detected Ciri's Elder Blood around 1267 and pursued her across dimensions. When Ciri was transported to the Aen Elle world, she was given an ultimatum by the elven sage Avallac'h: bear a child with King Auberon to reintroduce Elder Blood to the Aen Elle lineage, or remain trapped. Ciri refused and eventually escaped with the help of unicorns.
In The Witcher 3, the Wild Hunt invades the Continent with a full military force, attacking Kaer Morhen and pursuing Ciri to the Isle of Undvik. Their defeat at the end of the game removes the primary external threat to Ciri, which is part of why The Witcher IV can focus on her new life as a witcher rather than another chase narrative.
Status in The Witcher IV
With Eredin dead and the Wild Hunt's leadership destroyed at the end of The Witcher 3, the organization is effectively disbanded. Whether any Aen Elle elements appear in The Witcher IV has not been confirmed by CDPR.