Technically, Remote Play on Android is only meant to work on Sony's Xperia smartphone and tablet. Now, someone's got it working on any Android device, and with full wireless controller support.
The new APK (Android application package) can be found here with full instructions, and can be seen running Destiny and Dying Light on a Samsung phone and tablet in the videos below. It looks fairly simple to install, however [serious voice] word of warning: Android stuff varies wildly so you're on your own if you want to install this thing. Do it at your risk entirely. Especially as this isn't exactly an officially app, and step two of the instructions states you have to "Enter Custom Recovery, Flash ZIP and Reboot" to get it working.
If you are prepared to take the risk then this is what Destiny looks like on a tiny phone, spoiler: it's all buttons:
And here are a full set of instructions on how to get it running, including full wireless controller support. On a tablet, with a DualShock 2, things looks a lot more workable:
PS4 Remote Play for Android - Script Kitty