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Being a pretty uncluttered and stock Android device, the Play Store and Google services are the pre-installed options when it comes to video and music.
Music
The Google Play Music app is a fairly well integrated offering where you can listen to streaming or downloaded songs using your Google Play All Access subscription should you have one, or from the 20,000 songs Google allows you to upload to your account.
Music stored locally is also browsed through the app and can be played simply and quickly.
When music is playing, the track artwork populates the lockscreen background, with pause and skip track controls also available. It is a really bold and attractive effect.
The actual purchasing of music is done through the Play Store, so you will get taken there if you want to buy some tunes.
If you want to listen to music through an alternative service, the Moto X will handle that just fine and as more and more apps support the placement of artwork on the lockscreen, it normally looks just as good too.
When listening to your music, the single mono speaker does a decent job, being loud and actually of reasonable quality.
It is easily good enough to listen to podcasts through if that is your thing. Quality through headphones is average with minimal noise but the biggest issue is that the volume simply does not go high enough.
There is a graphic equalizer in the Google Play Music app on the Moto X which also has a few effects such as 3D stereo and Live Stage. Frankly, it is rather basic and generally does more to muddy the sound than improve it, but at least the option is there.
Movies
The Google Play Movies and TV app, besides being a mouthful, is where you go to get movies and TV shows. Again, it takes you to the Play Store to make your purchases, but then the media can be streamed or downloaded for offline viewing.
Video quality is high, and the screen on the Moto X lends itself well to watching movies. Obviously a tablet will give a more immersive experience, but I would be happy to watch for hours on the Moto X if I had to.
Despite apparently older hardware in the Moto X, it has no issues playing any games you can find in the Play Store at the time of writing. Gaming does take a heavy toll on the battery but everything works nicely and the phone doesn't get uncomfortably hot. Google Play Games is pre-installed on the Moto X, but it remains sparingly used by game developers.
The biggest issue with all media work on the Moto X is its limited storage capacity. In the UK, only the 16Gb model is currently available and with no expandable storage, it can fill up fast especially with larger games and movies.
The Moto X supports USB OTG which allows you to plug in a USB memory stick if you buy the right cable, so that could be an option if you want to watch lots of movies.