How to install TeX on Android phones?

I am the author of TeXLive for Android. I have provided an .apk file for Android, but I have not added XeTeX to my app, due to the large size of the xetex binary. You can get XeTeX from here: http://texlive-for-android.googlecode.com/files/tl4a-2013-06-18.tar.xz. I am now testing my GUI of tlmgr, which is written completely in Java.

The next version of my App will add biber and Vim 7.4 in 2014. A TeX editor for my App is now under development.

There is work to implement TeXLive 2012 for Android. The development site provides information on progress as well as access to downloads. The code is still experimental but might be worth a try. Otherwise the existing solutons are similar to VerbTeX and may involve web-based LaTeX processing.

Just have a look here: TexPortal. This is an App for Android which runs fine on my Nexus 7 without the need for rooting my device (this was important for me). If you download all the packages you don't need an internet connection to compile the documents. Most of the time I use it just for short letters, but for testing I compiled my diploma and my master thesis with this App without any trouble.