If you don’t own a Moto X, but envy it’s Active Display (which is similar to Nokia Glance on Lumia handsets), you can get one on your current Android device too using this third party app called AcDisplay.
The app has been developed by XDA member AChep, and it lights up your phone’s display whenever a notification shows up and then stays alight for a definite period of time. It works both on phones with AMOLED displays and LCD displays. However, in the case of the latter, the entire screen lights up instead of just a part of it turning on. This also stresses the battery more on phones with LCD screens.
The app offers a number of customization features. It allows you to choose which apps do you want to select to show up notifications for. It also supports quiet hours in which no notifications are shown at all. You can also remove the solid background of the notification screen and replace it with a wallpaper. Then the app can also replace your lockscreen entirely.
It’s a neat app that currently supports only devices running on Android 4.4. The developer will be adding new features and support for lower versions of the OS in the future updates.
You can download AcDisplay from the Google Play Store here.