The storyline of After the Bomb introduces a post-apocalyptic setting centered on the Eastern United States, where most of the area is populated by the mutated animals that form the majority of society.
This would have merely resulted in a population mostly dominated by mutants if the leaders of the world's governments had not made the assumption that the disease was a bio-weapon sent by their enemies.
The game can be assumed to take place a generation or two after this apocalyptic event, which is referred to as "The Crash" or "The Death".
Though the second edition of After the Bomb is a standalone with many updated rules and an entirely updated back-story, it remains compatible with the following previously released expansions: The original edition of After the Bomb was a supplement to Teenage Mutant Ninja Turtles & Other Strangeness, a game released in September 1985.
Marcus L. Rowland reviewed After the Bomb for White Dwarf #79, and stated that "It's all good fun, if you can accept the basic premises involved, but seems a little limited; I find the present-day setting of the original game more satisfactory, since it offers more opportunities for plot development and diversity.