Aethlem first appears in the Welsh prose tale Culhwch and Olwen, the longest and earliest of the surviving native Welsh prose tales and arguably the first extended Arthurian story ever written. The tale survives in the Red Book of Hergest and the White Book of Rhydderch, though the story itself is far older, born from tales told in halls and monasteries long before the quill touched parchment. In this tale, Culhwch, a prince born in a pig-run and cursed by his stepmother to love only Olwen, seeks the hand of the giant Ysbaddaden's daughter. Ysbaddaden, knowing that his own death is fated to follow his daughter's wedding, sets Culhwch a list of seemingly impossible tasks, among them the hunt for Twrch Trwyth, a boar that was once an Irish king named Taredd, transformed by divine punishment into a monstrous swine with venom-dripping bristles and a comb, scissors, and razor lodged between its ears.

To hunt this supernatural boar, Ysbaddaden demands a formidable pack. The only hound capable of tracking Twrch Trwyth is Drudwyn, the whelp of Greid. But Drudwyn alone is not enough. Ysbaddaden also requires the two whelps of the bitch Rhymhi, and two additional hounds named Aned and Aethlem. These hounds are no ordinary animals. In Welsh tradition, enchanted hounds were spoken of with the same awe as warriors. Aethlem and Aned are described as being as swift as a gust of wind and always triumphant when hunting, a pair of supernatural sighthounds whose speed and success set them apart from every other dog in Arthur's vast retinue.

The hunt for Twrch Trwyth dominates the latter half of Culhwch and Olwen and ranks among the most elaborate chase sequences in medieval literature. Arthur and his host travel to Ireland where they find the boar and his seven piglet-warriors. Menw son of Teirgwaedd flies over Ireland as a bird to spy on the beast, but Twrch Trwyth shakes himself and scatters venom, wounding the scout. The chase begins in earnest. Arthur's men drive the boar out of Ireland and across Wales, from Porth Clais through Carmarthenshire and the Preseli Mountains down to the Severn estuary. At every turn the boar turns on its pursuers, slaughtering knights and hounds alike, yet Aethlem and Aned keep pace, their wind-swift legs never faltering.

The hunt reaches its climax at the mouth of the Severn, where Arthur musters the Cornish and Devon men to halt the boar. The warriors manage to wrest the razor and scissors from Twrch Trwyth while he wades in the river, but the beast touches the riverbed and bolts away before they can seize the comb. The chase continues to Cornwall, where the boar causes more carnage than in all the previous battles combined. Finally Arthur's warriors drive Twrch Trwyth into the sea. The comb is retrieved, but the boar escapes into the waves. The tale ends with one of the most haunting lines in Welsh literature: it was never known from that day onward to what place the boar went, and Aned and Aethlem with him. The two wind-swift hounds vanished into the western ocean alongside the immortal quarry they were born to pursue.

Aethlem occupies a unique place in Arthurian tradition as one of the few named hounds whose story ends not in death but in mystery. Unlike Arthur's own hound Cafall, who left his paw-print in stone at Buelt and is remembered in the ninth-century Historia Brittonum, Aethlem leaves no monument, no grave, no trace upon the landscape. Its legacy is the chase itself, the eternal hunt that echoes in every story of dogs who run too far. In Welsh folklore, the Cwn Annwn, the white hounds with red ears who ride with the Wild Hunt, escort souls to the Otherworld; Aethlem and Aned, disappearing into the sea with a transformed king, stand at the boundary between the mortal hunt and the supernatural chase, between the world of living warriors and the realm where the hunted never die and the hunters never rest.