Valyrian steel was invented in Valyria and was used to make weapons and various other items of unparalleled quality. Being spell-forged steel, it is the spells and magic that make the steel special.
Valyrian steel, possibly forged with dragons, was manufactured in the Valyrian Freehold of old. Valyrian steel blades are lighter, stronger, and sharper than even the best castle-forged steel, and feature distinctive rippled patterns similar to real-world Damascus steel, the mark of steel that has been folded back on itself many thousands of times. Most Valyrian steel blades in Westeros are treasured heirlooms of noble houses, each with its own name and storied history. Valyrian steel was always costly, but it became considerably more so when there was no more Valyria, the secret of its making lost with the Doom.
Only the greatest weaponsmiths can reforge swords from existing Valyrian steel, making those remaining weapons highly treasured and extremely rare. The blacksmiths of Qohor claim to know how to reforge Valyrian steel.
Suits of armor can also be fashioned of Valyrian steel. Such armor is worth a kingdoms fortune and is exceptionally rare, no armor of valyrian steel has been seen for 400 years since the Doom and no one in Westeros possesses such armor. 
A Game of Thrones
A catspaw tries to assassinate Bran Stark with a Valyrian steel dagger, but he is instead slain by Summer. Bran's mother, Catelyn Stark, show the dagger to Petyr Baelish, who claims to have lost the dagger in the tourney on Prince Joffrey's name day.
A Storm of Swords
Lord Tywin Lannister has Tobho Mott, a blacksmith trained in Qohor, reforge Ice into two new Valyrian blades. The first, Widow's Wail, is given to King Joffrey I Baratheon as a wedding gift by his grandfather, Tywin. Joffrey chooses its name from the shouted suggestion of an unnamed guest. Following Joffrey's death at his wedding feast, ownership of Widow's Wail presumably passes to his younger brother, King Tommen I.
A Feast for Crows
A Dance with Dragons
The Winds of Winter
Euron Greyjoy is seen by his captive brother Aeron in a suit of black scale armor like nothing Aeron had ever seen before. Dark as smoke, but Euron wore it as easily as if it was the thinnest silk. The scales were edged in red gold, and gleamed and shimmered when they moved. Patterns could be seen within the metal, whorls and glyphs and arcane symbols folded into the steel. The revelation dawns on the shocked Aeron that the armor is forged of valyrian steel and that Euron has indeed been to the ruins of Valyria. 
List of known Valyrian steel blades
Blades known to still exist:
- Heartsbane, the ancestral two-handed greatsword of House Tarly, currently in the possession of Lord Randyll Tarly.
- Lady Forlorn, the ancestral sword of House Corbray, currently in the possession of Ser Lyn Corbray.
- Longclaw, the ancestral Valyrian steel bastard sword of House Mormont. Currently in the possession of Jon Snow.
- Nightfall, the ancestral blade of House Harlaw and currently wielded by Ser Harras Harlaw.
- 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.
- Red Rain, the sword of House Drumm, which was stolen by them in a raid. Given the name and coloring, possibly the ancestral sword of House Reyne.
- Widow's Wail, one of two Valyrian blades reforged by Tobho Mott from Ice. Following Joffrey Baratheon's death, ownership of Widow's Wail has presumably passed to his younger brother, Tommen.
- The dagger with a dragonbone hilt wielded by Bran Stark's failed assassin, and currently in the possession of Petyr Baelish.
- Valyrian steel arakh owned by Caggo.
- Valyrian steel axe reputedly possessed by House Celtigar.
Blades with known fates:
- Ice, the ancestral two-handed greatsword of House Stark. Following Eddard Stark's execution in King's Landing, it is reforged into two longswords (Widow's Wail and Oathkeeper).
Blades with unknown fates:
- Blackfyre, the sword of Aegon I Targaryen. Carried by all Targaryen kings until Aegon IV, who gave it to his bastard Daemon, 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. Its last known owner was Brynden "Bloodraven" Rivers.
- Lamentation, the ancestral sword of House Royce, lost in the Storming of the Dragonpit.
- Orphan-Maker, the ancestral sword of House Roxton. Its last known owner was Ser Jon Roxton.
- Truth, a Valyrian steel sword last carried by Moredo Rogare of Lys.
- Vigilance, the ancestral sword of House Hightower. Its last known owner was Lord Ormund Hightower.
- A small number of maesters, including Maester Luwin and Archmaester Marwyn, have Valyrian steel links in their collars, representing their study of magic and occultism. Marwyn also has a ring, a rod and a mask of Valyrian steel.
- Dragonbinder - a dragon horn banded with red gold and Valyrian steel.
- The crown worn by Aegon I Targaryen (and a few other kings), embedded with rubies.
Valyrian steel blades were scarce and costly, yet thousands remained in the world, perhaps two hundred in the Seven Kingdoms alone.
– thoughts of Tyrion Lannister
A man who bears Valyrian steel should use it for more than scratching his arse.
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
- A Game of Thrones, Chapter 2, Catelyn I.
- So Spake Martin: Producing Valyrian Steel, March 11, 2001
- A Game of Thrones, Chapter 72, Daenerys X.
- A Storm of Swords, Chapter 32, Tyrion IV.
- Batlicon Reading notes
- A Game of Thrones, Chapter 18, Catelyn IV.
- A Game of Thrones, Chapter 65, Arya V.
- A Game of Thrones, Chapter 60, Jon VIII.
- A Storm of Swords, Chapter 60, Tyrion VIII.
- A Storm of Swords, Chapter 72, Jaime IX.
- A Feast for Crows, Chapter 5, Samwell I.
- A Dance with Dragons, Chapter 7, Jon II.
- A Dance with Dragons, Chapter 60, The Spurned Suitor.
- Batlicon Reading notes
- A Feast for Crows, Chapter 19, The Drowned Man.
- A Dance with Dragons, Chapter 25, The Windblown.
- A Storm of Swords, Chapter 36, Davos IV.
- The World of Ice & Fire.
- The Princess and the Queen.
- The World of Ice & Fire, The Quarrelsome Daughters: Myr, Lys, and Tyrosh.
- A Clash of Kings, Chapter 28, Bran IV.
- A Feast for Crows, Appendix.
- A Dance with Dragons, Chapter 3, Jon I.
- So Spake Martin: The Process of Making Valyrian Steel, November 06, 2002
- So Spake Martin: On Valyrian Steel and Twist Endings, March 16, 2008