Motorola Moto X, lauched in 2013, has been disadvantaged since the release of the official Lollipop. Because of the out-of-date Snapdragon S4 Pro chipset, the Android updates requires some more tweaking before their launch and Moto X was always the most recent of the Moto line on the update queue.
Android 5.0 Lollipop update to Moto X (2013) got official a about a month ago, after a some obstacles and soak tests. In Brazil, today, begins a new soak test, and this time for the most recent Android 5.1 Lollipop OS.
On the Moto X, the 5.1 Android is already available and it brinsg improvements at stability and usability. It provides a better control over notifications and interrupts, the camera gets a better performance and Android system, plus some bugs has been fixed.
in Brazil, a similar update is now being developed for the first generation od Moto X, and if it all works out, in May it should be launched worldwide. Motorola is now committed to offer regular updates for Moto X (2013) until the end of 2015, so that more updates should be available later this year.