With Android L, you can easily record high resolution videos of your phone or tablet’s screen without having to root the device. Android Kitkat too allowed screen recording but with Lollipop, the process has become almost as easy as recording screencasts on your desktop - you launch an app (there are several alternatives to choose from), hit the record button and everything that’s on your screen, including touches, will be captured as a MPEG-4 video.
A quick search on the Google Play store returns a dozen Android apps that support screen recording for Android v5 or later.
Some apps are free while others are paid but they mostly offer a similar set of features. You can record the screen as well the on-screen touches so the viewer has a better idea about how you are interacting with the apps. They can record the external microphone audio but none of the apps I tried allowed recording of internal system audio. Maybe that is a limitation of the Android platform.
The most popular option is Mirror that will not only record your Android screen but it can also mirror your phone on to your desktop using AllCast Receiver, a free app for Chrome. There are no complicated settings to choose from, the recording is smooth but the big downside is that the app adds a fairly big watermark and you do not have option to disable it.
Shou.TV is another app than can record and also live cast your phone screen to the desktop without the watermark. It is the only app that can save the video in multiple formats including MKV, AVI and MOV. There’s however a lag when casting the screen on the desktop that makes it less usable.
The screen recorders from Rivulus, Hecorat and Misty also let you record the Android screen in multiple resolution including 1280x720 and 1920x1080 pixels at 30 frames per second. The recorded screencast can display touches, there are no ads and you can record videos of unlimited length. These apps do however add their icons in the notification window while the recording is in progress.
Telecine is an open-source Android screen recorder with a minimal and uncomplicated interface. It displays a 3-second countdown so you have enough time to hide the actual recorder app from the screencast. Also, you can stop a recording by simply tapping an invisible zone on your screen which is more convenient that tapping the app in the notification bar.
Another app in the category is SCR that offers a unique feature - it can add the picture-in-picture effect to your screencasts. That means it can use the front camera of your phone and overlay a live video of yourself on the screencast. The app is freemium and you need to upgrade to remove the watermark or to increase your screencast length which is limited to 3 minutes. [Update: Developer has removed the app from the Play Store]
I also liked Rec. that has a very clean interface and allows you save your settings as separate presets. You can turn off the screen and it will stop the current recording session. You do however need to upgrade to show the screen touches and for recording the microphone audio.
This screencast video was recorded on a mobile phone running Android 5.0.1 and rendered as an animated GIF
Most of the screen capture programs for Android are similar but my absolute favorite is Telecine - it has just the features you need packed inside a simple interface. Also, there are no time limits, no ads and no watermarks in the recorded screencasts. I would also recommend Mirror not for screencasting but if you are looking to mirror your phone screen on to your desktop computer.