Callandor is a male sa'angreal in the form of a crystal sword. It is sometimes called the Sword That Cannot Be Touched or Sword That Is Not a Sword, due to the fact that it was sealed behind powerful wards of the One Power that enabled only the Dragon Reborn to touch it, and due to the fact that it's primary purpose is to act as an angreal, and not a sword (though it can still be used as one).
It was one of the last sa'angreal created in the Age of Legends, yet it was made with flaws: unlike other angreal and sa'angreal, there is no "buffer" to prevent the user from drawing more of the One Power than he can safely handle. It was also theorized to magnify the effect of the Dark One's taint on saidin upon the user, causing erratic behavior and thoughts. As such, before the removal of the taint from saidin, the only way to use Callandor safely is within a circle of two women and one man, with a woman melding the flows. However, even before the removal of the taint, it was wielded quite effectively by Rand al'Thor alone on a number of occasions.
The Prophecies of the Dragon indicated that Callandor needed to be used during Tarmon Gai'don to battle the Dark One. It is interesting to note that Rand al'Thor has had a large number of experiences with Callandor in which he spontaneously wielded unfamiliar or sometimes brand new weaves of the Power. With the Power flowing through it, it also had the distinction of being the only object or ability in the series that could cleave balefire in the real world, though a specific weave known as The Flame of Tar Valon was able to counteract it. There are only two more powerful sa'angreal that a man can use: the male half of the Choedan Kal, and Sakarnen, a scepter that eventually came into the possession of Demandred, which was later used by M'Hael in the Last Battle. Callandor is also unique in that it is the only known object in existence with the ability to amplify one's ability to draw upon the True Power, access to which is typically controlled strictly by the Dark One. This aspect of the weapon, along with it's lack of a Power buffer, were crucial in defeating the Dark One.
Callandor was made shortly before or during the Breaking of the World. After learning of the Foretellings of the Prophecies of the Dragon, the Aes Sedai of the time built the Stone of Tear to safeguard it. They placed it in the central Heart of the Stone, surrounded by powerful wards of saidin and saidar to prevent anyone other than the true Dragon Reborn from claiming it. These wards were so effective that not even the Forsaken could circumvent them.
In 999 NE, the Dragon Reborn finally claimed and used it against Ishamael. During this battle, its ability to deflect balefire was showcased, as well as Rand somehow instinctively countering all of Ishamael's reality bending in Tel'aran'rhiod while wielding it. During a later assault on the Stone, he used it to unleash a deadly weave upon the Trollocs and Myrddraal, destroying them utterly, though he had no idea how he did it and later could not replicate it. Before leaving for the Aiel Waste he thrust the sword into the floor of the Heart to make clear his intention to return. He did this both so that Tear would remain loyal to him, and because the amount of the Power that he could access through Callandor frightened him.
As part of Rand's offensive against the Seanchan in 1000 NE, Jahar Narishma was dispatched to Tear to retrieve Callandor. Whether this fulfills the prophecy that "who draws it shall follow after" remains to be seen, but so far Narishma has been loyal to Rand.
Rand used it to call a lightning storm down on the Seanchan army attacking Illian, but due to the design flaws, and the instability of the One Power around Ebou Dar after the use of the Bowl of the Winds, he killed some of his own men as well. Nevertheless, the Seanchan Ever Victorious Army was defeated. Rand forewent using it in the future, and preferred after that battle to use the male Choedan Kal, as it was far, far more powerful than Callandor and had none of it's flaws.
During the cleansing of saidin, Jahar Narishma used Callandor in a circle with Merise Haindehl and Elza Penfell, with Elza melding the flows. It was used to bombard the attacking Forsaken at long range, killing Osan'gar. After this, Cadsuane Melaidhrin gave Callandor to an Aes Sedai friend of hers to study further, as she had long been aware of a verse from the Prophecies of the Dragon that indicated to her that Callandor specifically would be needed at Tarmon Gai'don.
During a meeting with the Borderland rulers, Rand drew it from a sheath on his back as proof that he was not a false Dragon.
Afterwards, Callandor's ability to amplify the True Power was discovered, an ability upon which Rand formulated his plan to repair the Dark One's prison. When Tarmon Gai'don began, Rand took Callandor with him to Shayol Ghul, and there he engaged Moridin in an ordinary sword fight. Near the end of their duel, Moridin cut his own hand, causing Rand pain through their link and forcing him to drop Callandor. Taking up the crystal sword, Moridin discovered it's ability to act as a sa'angreal for the True Power, but when he attempted to use it to destroy Rand and himself, Moiraine and Nynaeve used Callandor's flaw to entrap Moridin in a link. Linking with Moridin and the two women, Rand was able to use the True Power from Moridin, saidin from himself, and saidar from the two women to repair the Dark One's prison. Coating his weaves of the One Power with the True Power in order to keep the Dark One from touching either half of the One Power and tainting it as he had with saidin, Rand permanently sealed the Bore.