Although some of Motorola's newer phones are starting to get Android 5.1, the first generation Moto G is only now getting the Lollipop OS upgrade. However, it's the older Android 5.0.2 version and not Android 5.1.
Android Lollipop was a major upgrade from KitKat, both in terms of UI and in terms of under the hood changes. Google refreshed Android's UI with the "Material Design" language and added more smooth animations to the system's operations.
There were also many architectural improvements, such as replacing the Dalvik runtime with ART (Android Runtime), which quickly compiles the applications to native code, thus improving the performance and battery life of the device. However, there are some indications that the next version of Android will receive an even bigger upgrade to the Android Runtime.
The camera API was also overhauled in order for it to communicate much faster with the camera hardware. There were several security improvements and feature additions as well, such as the Smart Lock, which pairs the phone with another Bluetooth-enabled device in order to keep it unlocked as long as the two are near each other.
The Android 5.0.2 update should appear as a notification, which you can click on and follow these instructions:
- Select "Yes, I'm in."
- After the software is downloaded, select "Install now."
- After the software is installed, your phone will restart automatically.
- Your phone is now updated.
If you haven't received the system upgrade notification yet, you can manually check for it in system Settings > About phone > System updates, and if the update is available the above instructions will apply.
If you haven't received anything yet, then it's possible Motorola is rolling out the update in stages in different countries, and your update could be arriving soon.