If you're the owner of a Google Play Edition Moto G, your update to Android 5.1 has begun rolling out. Though these things go out in stages, you can always check manually for an update, or if you're too impatient, you can download and flash the OTA manually using the link to Google's server at the bottom of this post.
The build is LMY47M and the OTA clocks in at a fairly hefty 171 MB. As for what's new, you get all the assorted goodies that Google has added in 5.1 with the plain stock Android experience from Nexus devices. There are presently no rumblings of any other GPE devices receiving Android 5.1, but since they have all historically come around the same time, it's probably safe to say we'll start seeing them sooner rather than later.
OTA Zip File: LMY47M from LRX21Z