Last year's Android update to 5.0 (otherwise known as Lollipop) came out kind of slow, even to the newer Android devices. Update 5.1 was intended to fix a lot of bugs that came with 5.0, and this update has been slow to update as well. Especially when it comes to getting the Android 5.1 Lollipop update on the first and second generations of the Moto E, Moto G, and the Moto X.
1st and 2nd Generation Moto G
SlashGear states that the original Moto G LTE, not the first Moto G, will be attaining Android 5.1 Lollipop "this afternoon". Please keep in mind that this report is two days old, which means that if you are using this device, it should be available. The unlocked version of the device will be first, and then carrier versions, so you might not have access to Android 5.1 just yet. This report did say that all Moto G models are expected to jump to Android 5.1 Lollipop before the end of the month.
1st and 2nd Generation Moto X
A report from the International Business Times says that the Moto X from 2014 and the Moto X from 2013 are currently receiving the Android 5.1 Lollipop update.
The 2nd Generation Moto X has reached full deployment stage for AT&T and Verizon users of the this phone. This is according to David Schuster, Motorola's senior director of software product management and has kind of become the head spokesman for this issue with the 5.1 update. By the way, if you have the Moto X 2nd Gen Pure Edition through T-Mobile, then the Android 5.1 Lollipop update was available to you as early as June 26.
As for the first generation of the Moto X, the Android 5.1 soak test has begun for Verizon and AT&T, which means that it will be available for users of both those subscribers soon. So far, there doesn't seem to be any word about T-Mobile and Sprint.
1st and 2nd Generation Moto E
According to Motorola, the 5.1 update for the Moto E, both first and second generation, should really be available already, and you can check out the Motorola customer help site here for the first generation Moto E and here for the second generation Moto E. If you have this phone with this carrier, check out your Settings and see if you can get it, and there are reports that the 4G LTE version has it provided you are with Cricket.
Perhaps the bigger question that consumers will have is when will my device be receiving Android M? This is the latest version of Android that was unveiled at Google I/O Developer's Conference, and it doesn't have a decimal designation or a sweet treat named after it. Android M will be out sometime during the fall on the latest Android devices, and it will probably be another slow rollout with that.
In summary, it looks like the rollout of Android 5.1 on Moto phones is kind of slow, but it looks like it will eventually arrive on both generations of the Moto G, Moto X, and the Moto E soon.