Developed and published by Bethesda, Fallout Shelter is a simulation/RPG that's based on the post-apocalyptic wasteland in its Fallout game franchise. In this game, you play as a shelter overseer who's in charge of your very own vault. The goal here is to have a thriving population of vault dwellers while protecting them against the dangers of the outside world, like the Deathclaw and raiders.
There are many "rooms" and facilities that you can build, people to staff these "rooms", and well, the vault is generally designed to be self-sustaining so you can generate food, water, electricity, and even basic defensive gear. However, if you want to get the best gear for your people to survive tougher enemies, you'll need to send them out into the wasteland to scavenge for items ranging from weapons to armor, or even junk that you can eventually convert into something more useful. Be careful though! Your scavengers can die if you don't bring them home safely. Some caution and common sense are important, I'd say.
Fallout Shelter is, without a doubt, one of the best spin-offs for a triple-A game. It's insanely fun and addictive, and you'll get to put your Overseer skills to the test and see how well you can manage a vault in a post-nuclear war.