Culhwch is given the task by Ysbaddaden Pencawr, the giant whose daughter Olwen Culhwch seeks, of obtaining the comb and scissors from Twrch's head. Later in the story it transpires there is also a razor secreted there. These implements are then to be used to cut and treat Ysbaddaden's hair (most of the tasks on the giant's long list are ultimately to do with this ceremony of hair-cutting). Further, Ysbaddaden states that the only hound who can hunt Twrch is Drudwyn, the whelp of Greid, and then goes on to list the requirements of the leash to hold Drudwyn, the only man strong enough to hold the leash, &c. Ultimately Ysbaddaden calls on Culhwch to seek out Arthur, Culhwch's cousin, to help him hunt Twrch.
Prior to the hunt, Menw son of Teirgwaedd is sent to verify that the comb and scissors are between Twrch's ears. He takes the form of a bird and flies to Twrch's lair, encountering the boar with seven piglets. Menw then tries to swoop down and snatch one of the implements from Twrch's scalp, but only manages to take one silver bristle; Twrch is agitated and shakes himself, scattering venom onto Menw, wounding him.
The hunt for Twrch takes up the greater portion of the latter half of Culhwch and Olwen, and it is described in great detail the geographical route of the pursuit, and those who take active part in it. Although it is Culhwch who is given the task, it is Arthur and his men who take the most prominent role in the chase, Culhwch having successfully enlisted his aid.