Short version: good story, let down by the ending.
The set-up is a good one: Boston-based tech journalist Miriam accidentally discovers that she is one of a small clan of people with an unusual genetic quirk which allows them to "world-walk" - i.e. hop to another universe in the multi-verse. That other universe happens to be considerably less developed than ours, being basically feudal, and Miriam's clan have made themselves wealthy and powerful in both worlds by some cunning exploitation of this talent, to achieve things that others in the respective worlds cannot.
I'm not going to give away what, exactly, but it's not entirely legal in this world.
Miriam drops into this misogynistic, backwards world like a match into gunpower, refusing to fit the social norms, shaking up carefully-balanced political alliances and generally causing trouble.
Meanwhile, one of the clan has defected, in this world, and the authorities are becoming aware that there's something weird going on and start trying to reassert control.
All of that, by the way, is the basic set-up at the start of the first book.
Stross handles a reasonably large cast of characters in several feuding families and governmental organisations quite well, and several of the novels end with major upsets in the respective worlds, but unfortunately I don't think the ending meets the build-up.
There are several problems.
First, the last book seems to lose entire factions, by focusing on others. It might be that they're taken out of the game in the previous book and I've just forgotten, but I'm not sure about that.
Secondly, some of it's emotionally flat, and rushed. The Bad Guys don't all get their just desserts in satisfying ways. What happens to them makes sense, but I want more from the author.
Worst of all, Miriam and co come up with a solution to the epic problem facing them at the end of the tale, but it's unbelievably callous, and it's completely out of character for Miriam to not even raise this as a problem.
It's a shame, because up to the last book, it was great. In blog posts, Stross has described Miriam as being the equivalent of the Dark Lord, in standard fantasy. Despite being a (sort of) Lost Heir, she's not there to re-establish the status quo, but to blow it away completely. Some of what she gets up to is a lovely extrapolation of what world-walking would mean.
Oh well. Still looking forward to Rule 34 and The Apocalypse Codex, which are from different series.