I am also interested in this topic. For the time being there seems to be a couple of options:
- Running Linux (Various distros) inside Android (Complete Linux Installer, Linux Installer, Linux Deploy apps)
- Running Ubuntu Touch natively (Perhaps also other distros) but there are some difficulties related to the drivers and documentation, specifically for the Shield Tablet.
It would be amazing if Nvidia would give support, even if unofficial to install any Linux distribution, even if its their own, in the Shield Tablet.
Also it would be amazing to have the possibility of a x64 CPU + Tegra X1 GPU combination and be able to install a full Windows (Not RT) operating system. I think this would be a great option for people who are not currently happy with the level of Gaming Performance offered by the current offerings.