Like WINE there was a project to run AmigaOS 3.1 software for Linux and other platforms but it was made into an open source operating system named Amiga Research OS or AROS. It is best run inside an emulator and while it is not a modern OS as Linux it can be downloaded and run inside of Linux and the downloads section has more. While it is not ready for prime-time yet it is a promising OS that is being ported to many platforms and uses the user friendly Amiga GUI we Amiga users grew up with.
OK maybe AROS is not modern enough for you, and you like Linux instead. Then you might like Anubis OS as it is a hybrid of AROS and Linux. Much like when Apple took NextOS (based on *BSD Unix and the MACH kernel) and Classic Mac OS to make Mac OS X, this project wants to take Linux and AROS and do the same thing.
For those who want the classic Amiga there is UAE the Universal Amiga Emulator that needs kickstart ROMs and boot disk images to work. You can buy them from the Amiga Forever software and the emulator comes with all the files you need plus other goodies.
For the classic Amiga 68K series it is recreated via the Minimig that uses SD cards instead of floppy disks. A must for retro computer hobbyists. AmigaOS 4.1 exists for PowerPC based SAM 440EP systems like the SAM 440Ep systems and parts sold here. I am not associated with Amiga Kit or Amiga Inc. or any Amiga company. I am just an Amiga user since 1985 and very much into retro computing.
While the Amiga may seem dead, and it has been dead since 1994 when Commodore went out of business, the Amiga still exists in some form. The Amiga is dead and loving it, and the Anubis OS name is named after the Egyptian God of the Underworld, and when the Amiga repaired a floppy disk it renamed it as "Lazarus" the man Jesus raised from the dead. So the Amiga has a history of dying and coming back from the dead. It is the Kenny McCormick of computer systems and technology."