Introduction
Loki is the great trickster of Norse mythology, a shape-shifting, morally ambiguous figure who is a giant (jotunn) by birth through both his parents, yet lives among the Aesir gods as Odin's sworn blood-brother. His cunning repeatedly gets the gods out of trouble, and just as often gets them into it, culminating in his engineering of Baldr's death, for which he is bound in torment until Ragnarok, when he leads the forces that destroy the world.
This article follows Old Norse mythological tradition, chiefly the Poetic Edda and Snorri Sturluson's Prose Edda, noting where the two sources differ.
Family
Nature and role
Loki occupies an unusual, liminal position in Norse myth: neither fully Aesir nor straightforwardly a giant-enemy, he lives among the gods, takes part in their adventures, and is sometimes genuinely helpful (recovering Thor's hammer, rescuing Idunn he himself had endangered, fathering Odin's horse Sleipnir), while at other times his mischief causes real harm, as when he cuts off Sif's hair or orchestrates Baldr's death.
Shape-shifting
Loki is a skilled shape-shifter, appearing in myth as a mare (in which form he becomes pregnant and gives birth to Sleipnir), a fly, a flea, a salmon, and an old woman, among other forms, using transformation both to solve problems for the gods and to cause mischief.
Children
With his wife Sigyn, Loki fathers sons named in various sources. With the giantess Angrboda, he fathers three monstrous children who play central roles in the coming apocalypse: the wolf Fenrir, the World Serpent Jormungandr, and Hel, ruler of the underworld realm of the same name.
Baldr's death and binding
After orchestrating Baldr's death (guiding the blind Hodr's aim with the one weapon that could kill him) and then, in disguise, ensuring Baldr could not be ransomed back from the dead by refusing to weep for him, Loki fled the gods' wrath. Captured, he was bound to three rocks with the entrails of one of his own sons, and a serpent was set above his face to drip venom onto him continuously; his wife Sigyn catches the venom in a bowl, but must periodically empty it, and Loki's writhing in pain during these moments is said to cause earthquakes.
Ragnarok
Loki remains bound until Ragnarok, when he finally breaks free, leads the forces of chaos, including his own monstrous children, against the gods, and is fated to kill, and be killed by, the watchman Heimdall in the final battle.