Valyrian steel

Valyrian steel is a form of metal that was forged in the days of the mighty Valyrian Freehold. It is exceptionally sharp, tremendously hard-wearing and extravagantly expensive.

Valyrian steel swords

 * Dark Sister, a longsword of House Targaryen, now lost.
 * Ice, the greatsword of House Stark.
 * Longclaw', a longsword of House Mormont, now gifted to Jon Snow.

In the books
In the Song of Ice and Fire novels, the secret of forging Valyrian steel was lost in the Doom, making weapons made of it extremely expensive. Skilled smiths can reforge Valyrian steel weapons by melting down existing ones, but it's a difficult process.

Approximately 200 Valyrian steel weapons are known to exist in Westeros. Most of them are swords, but there a few daggers and axes as well. Valyrian steel can be identified by its dusky, unsual colour and the extreme sharpness of the blade.

In addition to the above, other Valyrian steel weapons known to exist include Heartsbane (House Tarly), Lady Forlown (House Corbray), Red Rain (House Drumm), and Nightfall (House Harlaw). Brightroar, the Valyrian sword of House Lannister, was lost in an expedition to Valyria centuries ago. An attempt to find it, led by Tywin's younger brother Gerion, apparently ended in failure, with no-one returning from the expedition. House Targaryen also possessed another Valyrian sword, Blackfyre, which was lost in the chaos following the First Blackfyre Rebellion more than a century before the events of the series.

Dawn, the sword of House Dayne, was not a Valyrian weapon but was held to have similar properties.