Culwhch was by most accounts the son of Goleudydd, who was overcome with madness, causing her to wander the countryside over the course of her pregnancy. She recovered her sanity as her labor began in a pigsty, but without sufficient time to remedy the situation. And so the hero was born amongst the pigs, and named Culwhch, “Son of Pig.” Culwhch's mother returned home but died shortly afterward.

Culwhch's father remarried a powerful woman who wished Culwhch to marry her own daughter. Culwhch refused, and his stepmother placed him under a curse, requiring that his future wife must be a girl named Olwen, the daughter of Yspaddadden, the dangerous chieftain of the race of giants. As far as love went, this was not a terrible curse, as Olwen's great beauty and demeanor were legendary, but her location was unknown and her father was a terrifying tyrant.

To locate his future spouse, Culwhch gathers together a band of skilled men, including Cei and Beddwyr, heroes who emerge later as transplants into tales of King Arthur. The party wanders in search of Olwen, and they are unsuccessful until they reach the home of a shepherd whose wife admits to being Olwen's hairdresser.

Although terrified of the giant Yspaddadden, the woman reveals that she is related to Culwhch and will arrange for him to meet his future bride. When Olwen arrives for her usual appointment, the woman introduces her to Culwhch. Olwen is immediately charmed, but she warns Culwhch that she cannot marry him without her father's consent. She further warns him that he must accede to any condition whatsoever her father may set and that flinching from any request will be fatal.

Culwhch and his party immediately set out for the giant's property. Unbeknownst to Culwhch, Yspaddadden labors under a curse of his own — that should his daughter marry and beget children, the giant will die. When Culwhch and his party arrive at the giant's castle, the giant attacks them with poisoned stones, which Culwhch and his band are able to catch and return to the giant. After this cycle repeats for three days, the giant relents and admits Culwhch to his court. He agrees to the marriage of the hero and his daughter, but sets strict conditions on the marriage, which cannot succeed unless Culwhch completes three impossible tasks.

The first task laid upon Culwhch is to sow flax for Olwen's bridal veil. Culwhch is led to a barren field, which the giant informs him was sown when he first took Olwen's mother for a bride. The field has so far failed to sprout. Culwhch is ordered to retrieve nine bushels of flaxseed from the field, burn the field, till it, resow it, and harvest nine more bushels of flax — all to be accomplished in one day. The giant is certain that Culwhch cannot accomplish the task, but Culwhch remembers his betrothed's warning, and assures that he can easily accomplish the task.

The Hunt of Twrch Trwyth

The second task laid upon Culwch by Yspaddadden is the accumulation of a great dowry, consisting of thirteen great treasures, including the magical sword by which he is destined to die. Culwhch affirms that these, too, will be easy to gather. The giant's final request is for a shave and a haircut, which can only be accomplished with a special razor, scissors, and comb, which conveniently reside between the ears of the great boar Twrch Trwyth, who, in parallel to the tales of Cuchulainn, can only be hunted with the aid of a magical hound that happens to belong to the long-disappeared Mabon ap Modron.

At this point in the cycle, King Arthur and his men inexplicably make an abrupt appearance to carry on the remainder of the tasks, although many of these tales have either vanished or been left to the imagination.

The flax is recovered by ants grateful to Arthur's companion Kai, who performs heroic deeds on their behalf. Arthur and his party locate and rescue the imprisoned Mabon, and the grateful demigod allows them the use of his magical hound.

The culmination of the story of Culwhch is in the hunt for Twrch Trwyth, the great boar. Like any proper boar in Celtic mythology, Twrch Trwyth is exceedingly large, powerful, and clever. Several attempts to acquire the barber tools through trickery are foiled. The magician Menw takes on the form of a bird and attempts to steal them but is nearly killed by the boar's poisonous barbs.

Twrch Trwyth proves impossible to do away with. All of Culwch and Arthur's forces are unsuccessful in killing even the piglets that accompany him. Arthur himself then battles the great boar for nine days without making any progress. At last, they attempt to negotiate with Twrch Trwyth, who informs them that his annoyance is now so great he intends to venture in Culwhch's lands and destroy them. The warriors follow him from one coast to another, and at last they manage to drive him into the sea, where they recover the scissors and accoutrements with the aid of Mannanan mac Lir.

Quests fulfilled at last, Culwhch returns to Ysbaddadden's castle, but instead of welcome, he is met with hostility. The foolish giant informs him that because his daughter's marriage spells his death, he will never allow her to marry. But Culwhch is now in possession of the sword that can kill the giant, and he promptly cuts off Ysbaddadden's head.