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.
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.
As for the Moto G, first and second generation, there has been any real changes since last week. A recent report that appeared on Android Central has given a report from Motorola's own David Schuster, who announced a lot of information about the availability of Android 5.1 Lollipop on various Motorola Moto devices.
For the Motorola G, 1st Generation with 4G LTE, the company is doing a full soak in Brazil Retail about a week ago. It is possible to go to the Motorola website and read that they are "excited to announce a new software update for the Moto G with 4G LTE by Motorola" and "this update brings Android 5.1 Lollipop to your phone along with other improvements". You should probably check your Settings right now if you are a user of this device.
Users of the Moto X, second generation, will be glad to know that the Android 5.1 Lollipop update has been rolled out on several U.S. carriers that include Verizon, AT&T, and U.S. Cellular. It is possible to update by checking the Settings and getting it now, according to Tech Times.
I suppose that leaves Sprint and T-Mobile not having the Android 5.1 Lollipop update on their Moto X, 2nd generation phones. This leads to the obvious question of when will Android 5.1 Lollipop arrive on Moto X, 1st generation (2013 edition) smartphones? According to Phone Arena, the retail version of the 2013 Moto X is on its way to the same updates, with David Schuster naming 14 countries now in receipt of the Android 5.1 update. The list includes Austrailia, Hong Kong, India, Kuwait, Malaysia, Oman, Qatar, Saudi Arabia, Singapore, United Arab Emirates, Belgium, Italy, Netherlands, and Spain. In other words, the 1st generation update should be on its way in the United States.
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.