Back on the 19th of June which was just last Friday, Motorola's David Schuster took to social media to out the fact that Android 5.1.1 updates were starting to roll out to Moto X 2013 owners in the U.S., Brazil, and Canada. This was a little more limited, and the updates were only reaching Rogers devices in Canada, and unlocked GSM models in both the states and Brazil. Prior to this update beginning though Motorola had stated on at least one occasion that Android 5.1.1 updates would be hitting devices in the next week or so if all things with the soak tests they started went well.
It seems like the soak tests went off without a hitch and as of today, in addition to the retail (unlocked) model of the 2013 Moto X in those listed regions above, Motorola is officially rolling out the Android 5.1.1 update to the unlocked models in other regions as well, globally, so if you have the original Moto X still you should be seeing the update sometime today or over the next few days. Keep in mind that software updates roll out in staggered batches, so if you don't see it today it shouldn't be long before it pops up, and you can always check for the software update manually if you like by navigating into the settings menu and then down to about phone, and then tap software updates.
Motorola is also officially rolling out the update to the 2014 Moto X, so it seems the only ones left waiting are the carrier models, (save for Rogers in Canada) and unfortunately there is no telling how long it may take for these since the push has to come from the carriers themselves in the end. With this update users can expect various different changes to take place, like swiping up to remove heads up notifications from the screen but letting it remain in the status bar until users dismiss it later. In addition to this and the other things that come along with this update, users can expect a number of bug fixes and improvements on their devices, so performance and overall user experience should see an improvement as well. If you're interested in the full set of changes, you can view the changelog at the source below.