In Divergent, one faction leader turns evil and tries to take control of all the factions. In Insurgent, the factionless (i.e., those without factions) take control from the evil faction leader. And finally, in Allegiant, another faction leader tries to get back all that control from whoever last had it. That's the story in a nutshell - Everybody fighting for control. Against that backdrop, they all find out that there is an outside world and other people like them and for some unknown reason, the people of these five factions and the factionless have been boxed into a community.
Of the three, I liked Allegiant best, but only by a small margin. Allegiant finally made sense of the world that author Veronica Roth created without much initial explanation. I didn't like how the first two books seemed to not give any hint of what is the deal with these people and all of a sudden, there is this whole mystery and scandal behind, revealed in the third book. But at least it all made sense to me, even if it was all too convenient. The writing in this one is just as unwieldy and the dialogues very sappy. It surprised me initially when I found that this book alternated between two characters - Tris and her boyfriend Tobias, even though the previous two books were from Tris' perspective alone. The third book is a little too late in the game to start switching narration styles, so I figured there was something more to that kind of decision. Which, when I found out, I didn't appreciate at all.
Anyways, long griping made short, this is a good series for a quick fun read, so long as you don't read too much between the lines. I feel there are more meaty series' out there that are more entertaining and logical. With better dialogues. If you haven't yet started this series, then you probably are not missing much.