Well there are 4 modes. 2 co-op and 2 competitive.
One mode is very similar to COD's zombies, except its on steroids, and you have to collect cases of ammo and guns to bring back to the safe house between rounds. And Alma is constantly walking around the map, and if you so much as look at her, she possesses you instantly. Its fun as hell.
Then there's F****** Run. Which is very unique. You got a team of 4, and the premise is simple. Your constantly being chased by an evil wall of smoke, which instantly kills you if its catches you. If one teammate dies, the whole team fails. You work through mass amounts of enemies to make it to each safe house all while running for your damn life from the cloud. Its chaotic and frenetic as hell.
Then theres a mode similar to VS in Left 4 Dead. 4 players, 3 on the same team, and one is randomly chosen to be the Possessed. The team works together to try to stay alive from hordes of enemies as long as possible, while the possessed dude tries to kill them in various ways.
Then theres another mode I havent played yet. All four mode require teamwork in order to do good. I love it. Would be a blast with friends thats for sure. I bought F3AR for the SP, as Im a fan boy of the series
But the MP is a HUGE surprise, and one that I can see myself playing for awhile.