Valyrian steel was manufactured in the Freehold of Valyria with dragonfire before the freehold fell. It is much lighter and stronger than regular steel. It cannot be made any more, no one knows the secrets to its forging since Valyria vanished.
Valyrian steel blades are lighter, stronger, and sharper than even the best castle-forged steel, and feature distinctive rippled patterns similar to Damascus steel. Most Valyrian steel blades in Westeros are treasured heirlooms of noble houses, each with its own name and storied history. Valyrian steel keeps its edge forever.
Only the greatest weaponsmiths can reforge swords from existing Valyrian steel, but the secret of creating such an alloy was apparently lost with Valyria, making those remaining weapons highly treasured and extremely rare. The blacksmiths of Qohor claim to know how to reforge Valyrian steel, and Tobho Mott did reforge Ice at the request of the Lannisters, in King's Landing.
List of known Valyrian steel blades
Blades known to still exist:
- Widow's Wail; One of two Valyrian blades reforged by Tobho Mott from Ice. The blade was made for King Joffrey Baratheon as a wedding gift by his grandfather, Lord Tywin. Where it was given its name from the shouted suggestion of an unnamed guest. Following Joffrey's death, ownership of Widow's Wail has presumably passed to his younger brother, King Tommen.
- Oathkeeper; One of two Valyrian blades reforged by Tobho Mott from Ice. The blade was made for Ser Jaime Lannister, but he has given it to Brienne of Tarth for use in her quest to locate Sansa Stark. The blade was given its name, Oathkeeper, at that time.
- Heartsbane, the ancestral two handed greatsword of House Tarly, currently in the possession of Lord Randyll Tarly.
- Longclaw, the ancestral Valyrian steel bastard sword of House Mormont. Currently in the possession of Jon Snow.
- Lady Forlorn, the ancestral sword of House Corbray, it is currently in the possession of Ser Lyn Corbray.
- Red Rain, the sword of House Drumm stolen in a raid. Given the name and coloring, possibly the ancestral sword of House Reyne
- The dagger with dragonbone hilt wielded by Bran Stark's failed assassin, and currently in the possession of Petyr Baelish.
Blades with known fate:
- Ice, the ancestral two handed greatsword of House Stark. Following Eddard Stark's execution in King's Landing, it was melted down and reforged into two longswords(those being Widow's Wail and Oathkeeper).
Blades with unknown fate:
- Blackfyre, the sword of Aegon I Targaryen. Carried by all Targaryen kings till Aegon IV who gave it to his bastard Daemon Blackfyre who rose in rebellion against the Targaryens, taking the sword's name for his house. Its whereabouts are currently unknown.
- Brightroar, the ancestral sword of House Lannister, lost when King Tommen II Lannister of the Rock sailed to Valyria and never returned.
- Dark Sister, the sword wielded by Visenya Targaryen. The last known owner was Bloodraven.
- Vigilance, ancestral sword of House Hightower. 
- Orphan-Maker, ancestral sword of House Roxton. 
- A very small number of Maesters have Valyrian steel links in their collars, representing their study of magic and occultism. Among them are Maester Luwin and Archmaester Marwyn. Marwyn also has a ring, a rod and a mask of Valyrian steel.
- Dragonbinder - a Dragon Horn banded with red gold and Valyrian steel.
Valyrian steel blades were scarce and costly, yet thousands remained in the world, perhaps two hundred in the Seven Kingdoms alone.
Valyrian steel is a fantasy metal. Which means it has magical characteristics, and magic plays a role in its forging. 
Valyrian steel was always costly, but it became considerably more so when there was no more Valyria, and the secret of its making were lost. 
References and Sources
- Producing Valyrian Steel. (March 11, 2001) So Spake Martin
- Game of Thrones, Season 4, "Two Swords".
- A Storm of Swords, Chapter 36, Davos IV.
- A Dance with Dragons, Chapter 25, The Windblown.
- The Princess and the Queen.
- A Clash of Kings, Chapter 28, Bran IV.
- A Feast for Crows, Appendix.
- A Feast for Crows, Chapter 5, Samwell I.
- A Dance with Dragons, Chapter 7, Jon II.
- A Storm of Swords, Chapter 32, Tyrion IV.
- So Spake Martin. The Process of Making Valyrian Steel. (November 06, 2002)
- So Spake Martin. On Valyrian Steel and Twist Endings. March 16, 2008