I don't wanna spoil too much but... first chapter starts off with the knights. You remember the woman speaking in the intro cutscene and how she has some guy shoot the viking with the arrow to make them keep fighting right when they looked like they were gonna call a truce? That's Apollyon. You start off as a warden, participating in part of her rise to power and ideology as she fights other lords and pushes back the vikings. That's chapter 1. Chapter two is where you play a viking as they rise up after those immediate events (which is where I am and about to start). Third chapter is the samurai faction, but I don't know much about that. But I can guess at where the story's going.
Obviously, you get to play as different characters that factions during those storylines. With the knights, I actually played only 3 of the units, but one of 'em was the new one and the one I didn't play was the one I mained during the beta, so I don't really feel cheated.
If there are any more chapters after those 3, I am not able to see 'em yet.
It's kind of annoying in that there's a second tutorial that pretty much is the same as the tutorial it makes you play when you first start the game. Other than that, it's pretty much what you'd expect. Dashing in and taking over zones, killing minion soldiers, and attacking captains and bosses. There's been one sort of escort mission, and there are a couple of places where you get to use the drop down to ambush an enemy below you. There's been an area where you were fighting on thin ice and you either had to use mobility or make it a part of your strategy. So there is some variety in location and stuff.
They also have hidden things to find/collect. Each level has some groups of barrels or boxes for you to break to find a particular item (an emblem or whatever I guess) and there are different things you can look at and activate to hear Apollyon give backstory and history, that are also tracked unlockable things. It's just rather simple stuff, but not all of 'em are obvious to find.
Leveling up in campaign and getting perks or things to activate is much faster than in multiplayer and carries across all the units you play as, so that helps the pacing along and gives you useful powers.
Also, the warden, the beginning character your play as for the knights has Akihiko's voice, and it kind suits his characterization perfectly.