It's a pretty interesting concept. It means it's really easy to knit together a user. One of the most fascinating concepts is this notion exposed by mbrace of "just in time" and "user specific" clusters. You can use a user's Azure environment to do distributed computation on their behalf (after getting them to agree to charges, of course) without exporting their data to a generalized cloud infrastructure.
This has a lot of potential for giving the user the best of both worlds. It's a hell of a lot more approachable than a DIY approach like Sovereign.
Not what you are asking about, but I find it very useful; Microsoft has a product called power BI which is a dashboarding/BI solution and you can create dashboards for Cortana.
A notable exception to this is HomeKit devices. While it's not close to what you'd want for a general third-party API, it does let you integrate some things. I've messed around a bit with using a server to fake being a HomeKit device to get some custom things working with Siri.
Either when I've got the app open/focused, or even when the app isn't running?