Nothing reigns consistently in Game of Thrones (and George R.R. Martin's "Song of Ice and Fire" book series that inspired it) except Valyrian steel, a magical sword material. Valyrian steel is, of course, extremely not real. But materials scientist Ryan Consell took a look at its chemistry anyway.
In the video below, Consell ponders what blend of iron, carbon, and other materials could possibly make Valyrian steel so special, based on characteristics ascribed to the magical steel in the books: a unique rippled pattern and incredible lightness, plus an ability to withstand regular fire:
One of the big contenders for Valyrian quality is spring steel, a low-alloy steel with carbon, silicon, and manganese. It's strong and durable. Of course, it lacks a certain je ne sais dragonfire, and can't withstand extreme heat, so there's no way it could actually work for the near-impervious swords. Air-hardened steel is better for the heat... but too heavy to match up with the Stark's favoured weapon material.
(Requisite moment of silence for Ned Stark, valar morghulis.)
Cosell writes about more possible materials on his blog, including the idea that it's not actually steel at all:
One possible candidate is that Valyrian steel is a metal matrix composite, or MMC. These employ a metallic framework, which provides some toughness and tensile strength to the material, and have a much harder material, like a ceramic, embedded into them which could provide that indelible edge.
In Martin's fantasy world, of course, Valyrian steel is created with much more than just metals -- it requires a spell and some Dragonfire. There's no way scientists could reproduce it. But it's fun to see how close we can get.