Made by the Dark Elves, they are infused with magic and power, and they have some independence, being able to choose their own masters. They were made long ago and none now live who know the craft. They were made for specific people, and once those people died the swords were passed to others. Once a Great Sword has a master, it can be dangerous for others to attempt to use it.
Alex is the master of Moon Slayer, one of the greatest of the Great Swords. Sindar has a pair of scimitar Great Swords, though not as powerful as Moon Slayer. More were made, but as of now, we don't know of them.