Casterly Rock is a stronghold owned by the Lannister family. It is a rich and powerful fortress, laying on the west edge of the Westeros continent, south of Riverrun. As of A Storm of Swords the fate of it is uncertain; Jaime Lannister, as a member of the Kingsguard, can hold no land, Cersei is female, and Tywin Lannister (now deceased) refused to give the rights to it to Tyrion Lannister, Tywin seemed to be leaning toward making Ser Kevan Lannister his heir if it could not be Jaime. Tyrion could have fought for his rights as heir, if he wasn't on the run for his father's murder.
Casterly rock sits on top of a gold mine, the source of much of the Lannister's wealth. The castle once belonged to House Casterly, but legends say it was swindled from them by the trickster Lann the Clever.