Post Apocalyptic fiction is set after a major catastrophic event such as a nuclear war, worldwide environmental disaster, impact event, resource depletion or other disaster that has a worldwide effect and generally brings about the end of civilization.
These stories can be set anywhere from immediately after such an event to a time when a pre-catastrophe civilization has been all but forgotten and faded to myth and legend.
Stephen King's Dark Tower Series
Abaddon Book's Afterblight Chronicles
William Tenn's Of Men and Monsters
Peter Heller's The Dog Stars
John Christopher's The Death of Grass