Motorola released the update for the retail (carrier free) version of the Moto X (1st Gen) today. You can find the release notes here. This update includes things like being able to use a custom phrase, rather than having to say "Okay Google Now", and now shows multiple notifications from the lock screen.
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Android 5.1 released for Moto X
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Installed on the wife's unlocked Moto X last night - haven't heard too many complaints other than "Ugh, it's different. I hate change." Hopefully she'll warm up to it. 
It seems to be a good upgrade. In my time using it, I've noticed that I'm getting better battery life when the phone is in standby; it has a better low power state. Of course, it seems to use as much battery as ever while being used. It also seems to be somewhat faster. I've been happy with the update, though it does take some time to get used to some of the changes.
I'd strongly suggest formatting your cache partition after upgrading (after any OS upgrade, not just this one), as items leftover in the cache from before the upgrade can cause issues. To format the cache partition, use the instructions for Lollipop here; while I realize that is the instructions for the 2nd gen, they seem to work and the instructions have changed slightly from Kit Kat. If you still have issues with lagging or battery, you might want to consider a factory reset to really clear things up.
I'd strongly suggest formatting your cache partition after upgrading (after any OS upgrade, not just this one), as items leftover in the cache from before the upgrade can cause issues. To format the cache partition, use the instructions for Lollipop here; while I realize that is the instructions for the 2nd gen, they seem to work and the instructions have changed slightly from Kit Kat. If you still have issues with lagging or battery, you might want to consider a factory reset to really clear things up.
You'll need to wait until 5.1 is released for the Verizon version of the phone. I haven't checked recently but the last I knew 5.1 is only available for the "retail" (carrier unlocked, unbranded) version of the phone.
You can sign up to be a beta tester on motorola.com, which might allow you to get the update a week or two earlier as part of a soak test; you can find the instructions here. If you have previously rooted your phone, you may still be selected. I know for the retail soak test, they wanted feedback both from people who had never rooted, and those that had previously rooted, their phones.