It is a very brutal game in terms of modelling entropy... Everything including the characters will rot or break eventually.
The die system uses three colors of d6s to tracks base attributes, skill and gear. You roll all of them and look for 6s. If you want you can 'push' rolls (reroll all not 6, or not 1s), but then all of those ones you roll on your base dice become trauma, and the ones on your gear dice go towards damaging/breaking your weapons. (A similar breakage mechanic exists for cover/armor)
If you get one 'success' that is typically enough, but each skills has a few 'stunts' you can spend extra successes on which makes for a surprisingly tactical game. (eg. You pass your 'endure' roll while hiking through a terrible blizzard, but another PC fails the original roll, as well as the 'push'. If you 'push' and reroll the other dice, you might get another success which you can use to help your friend succeed, or you might just incur several points of trauma as you try but fail to drag him to safety...)
On the plus side, it is by pushing yourself that you get mutation points to power your mutations, so yes you may be put on the edge of becoming fatigued/confused/broken in a fight, but now at least you can use your mutant power to eat that Zone Ghoul you just killed and save some rations.
This is a game in which the players can starve,die of dehydration, 'rot' or watch all of their People in the Ark get slaughtered if they don't build up their community.
Speaking of the Ark, this is the home of the People, your people, but the food is running out and your Elder is dying. There is a 'meta-game' wherein you develop the ark with what you find in the ruins, or perhaps move it entirely.
Finally, this game is almost literally 'no prep'. You should have an idea of what city you want to start the campaign in, and if you don't use New York or London you may have some map work to do.
Character creation is a quick point-buy system, aside from mutations which are entirely random. This speed of creation is important due to the horrific level of lethality inherent in the system and the genre.
Overall I can't think of a system that better emulates the post apocalyptic genre.