This is a post mostly for self-reference:

When you start a really long process (say, a backup) and forget to run it under a screen instance or using &, you can pause the process and resume it in the background with a couple of commands:

$ ./my_backup_script
^Z
[1]+  Stopped                 ./my_backup_script
$ bg 1
[1]+ ./my_backup_script &
$ disown -r

Running disown is important, because it tells the process to continue running after you close your current session.