Updated 28-Jun-2024
As of early 2018, ChromeOS and Desktop Linux have both crossed the 3% threshold. Android is approaching 50% for OS market share, and is in excess of that in terms of new devices. Heady times for the Linux Kernel indeed. While Android uses the Linux Kernel, nearly everything else in Android is customized, and therefore it doesn't have any distribution linneage to speak of. ChromeOS is derrived from Gentoo Linux, a custom build linux distribution.
As far as Desktop Linux, it is led by Ubuntu, a Debian-based distribution, Mint, an Ubuntu-based distribution, Debian itself, and Fedora, a member of the Amazon Linux/CentOS/Red Hat family. Server-side there is: Amazon Linux/CentOS/Red Hat, Debian/Ubuntu, and Suse. Arch Linux is also considered a popular Desktop/Server though it is hard to find stats that show this.
Linux-based/derrived operating system interoperability is interesting and progressing, especially between ChromeOS and Android, as well as the possibility of support for running linux apps using Crostini on ChromeOS. Our guess is they will run inside the same kind of environment as Android apps.
Crouton Dual-Boot ChromeOS and Linux
This is an oldie but goodie, essentially running Linux in a chrooted environment on top of ChromeOS, pretty much how Android runs, I am guessing.
Firmware for intel Chromebooks
ARM not supported, but some nice coreboot/firmware at Mr. Chromebox.
Linux on Chromebooks
The main focus is on intel, which is where Linux has its expertise. A popular choice is GalliumOS, but the hardware requirements are limited to intel.
Rooted ChromeOS + Android Apps
The easiest approach for a bit more control and functionality is a combination of Developer Mode which provides root access, as well as Android Apps. Quite useful and not too much fiddling needed. See more about ChromeOS apps and configuration.