Fallout 1 is set in the year of 2161, in the Core Region, specifically in and around the state of California.
The player character, named the Vault Dweller is a resident of Vault 13 in the year of 2161. The Overseer of the vault discovers that the vault's water chip which is responsible for recycling the vault's water and keeping it fresh has broken, and they do not have the parts to fix it. He sends the Vault Dweller out into the wastes to search for a new water chip, before the vault runs out of drinking water, which is in 150 days time.
After returning successful, the Overseer tasks the player yet again with the destruction of a super mutant army, led by the Master who wants to unite the wastes and turn it's inhabitants into super mutants.